More equal but less mobile? Education financing and intergenerational mobility in Italy and in the US

Transcription

1 Journl of Publc Economcs 74 (1999) 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, 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 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.: ; fx: E-ml ddress: [email protected] (A. Ichno) / 99/ $ see front mtter 1999 Elsever Scence S.A. All rghts reserved. PII: S (99)

2 352 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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).

3 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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, ) 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.

4 354 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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.

5 D. Checch et l. / Journl of Publc Economcs 74 (1999) Tble 1 Inequlty mesures for Itly nd the US Mesure Itly US Itly US Fther Fther Son Son percentle dfferentl Reltve men devton Coeffcent of vrton Stndrd devton of logs Gn coeffcent Atknson (e 5 2) Thel entropy 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 C Fther C Fther C Fther C Abs. freq 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 C Fther C Fther C Fther C Abs. freq 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.

6 356 D. Checch et l. / Journl of Publc Economcs 74 (1999) Tble 4 Income clsses for the Unted Sttes nd for Itly Clss 1 Mnmum Medn Mxmum Clss 2 Mnmum Medn Mxmum Clss 3 Mnmum Medn Mxmum Clss 4 Mnmum Medn Mxmum 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 ( ), 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).

7 D. Checch et l. / Journl of Publc Economcs 74 (1999) Tble 5 Sclr ndctors of moblty for nterclss trnston mtrces Itly US Eq. opp. ML ul2u k 2 tr(p) MT 5]] k (1/(k21)) MD udet(p)u MB 5 o oj fju 2 ju MA5 o oj fjuw 2 Wju 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 See for exmple Tremn nd Yp (1989).

8 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 (0.03) (0.03) (0.03) (0.03) Fther wth college degree (0.09) (0.09) (0.04) (0.05) Son wth college degree (0.05) (0.05) (0.03) (0.03) Fther s ge (0.002) (0.002) (0.002) (0.003) Son s ge (0.001) (0.001) (0.004) (0.003) Observed prob Predcted prob Pseudo R Log-lkelhood Smple sze 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)

9 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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 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 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.

10 360 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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 Son Lmt 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 E Fther E Abs. freq 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 E Fther E Abs. freq 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.

11 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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]] p 22 /p21 k 2 tr(p) MT 5]] k 2 1 MB 5 o oj fju 2 ju 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.

12 362 D. Checch et l. / Journl of Publc Economcs 74 (1999) Tble 11 Itly: trnston probbltes from less thn hgh school to hgh school or 1 Son E1 Son E2 Abs. freq. Fther E Fther E Abs. freq 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) 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 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 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.

13 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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 N51666 Son Unted Sttes Fther N51050 Son 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 Source: Pnel Study of Income Dynmcs.

14 364 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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.

15 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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 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).

16 366 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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 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 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 /4/94, Testo unco delle dsposzon legsltve vgent n mter d struzone, reltve lle scuole d ogn ordne e grdo.

17 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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 %. The stndrd errors of (comprble cross countres) textscores for redng nd nrrtve cpbltes re, respectvely, 3.4 nd 3.6 n Itly nd 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 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.

18 368 D. Checch et l. / Journl of Publc Economcs 74 (1999) nequlty nd ntergenertonl moblty. Frst, however, we wnt to sketch nformlly the story tht our model proposes 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, , 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.

19 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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.

20 370 D. Checch et l. / Journl of Publc Economcs 74 (1999) 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) 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

21 D. Checch et l. / Journl of Publc Economcs 74 (1999) the test of the educton system. If the person decdes to go to school, nd fls, then he knows hs tlent ws low; on the contrry f he succeeds he knows tht t ws hgh Preferences The utlty of ech person depends on lesure of the frst perod, consumpton of the second perod c t11, nd term whch descrbes the expected utlty from the qulty of the educton whch s left to the son. The expectton s tken wth respect to the belef nt11 tht the person hs on hs son s tlent, whch s not 38 known wth certnty. Formlly: U(n t, c t11, n t11, e t11) 5 log nt1 log ct11 1 nt11 log e t11 (4.2) The budget constrnt of ech person wll depend on the nsttutonl rrngement for the provson of educton: so we shll del wth t n the next secton Two nsttutons for educton fnncng As n Glomm nd Rvkumr (1992) we consder two dfferent possble nsttutonl rrngements for the provson of educton, tht s n the context of our model, for the determnton of the quntty e. t The frst s purely prvte regme, where e s decded by the fther, nd pd t out of hs ncome. The second regme s pure stte school system. The qulty of educton provded to ech chld s the sme, nd s decded s follows. A tx rte t [ [0, 1] s voted n ech perod, nd chosen ccordng to mjorty rule. The tx rte ppled to the totl ncome gves n mount spent on the collectve educton: E 5 t H t t t (4.3) We cn now stte the budget constrnt formlly. In the cse of prvte school system, the ndvdul s fcng the two constrnts: n # 1; c 1 e # h ; t t11 t11 t11 whle n the cse of the stte school system, wth tx rte t t11, we hve: 37 The lesure term s ntended to cpture the opportunty costs of the eductonl nvestment borne by the son. 38 A stndrd procedure to model ltrusm s to ssume tht ndvdul utlty postvely depends on bequests (see Glomm nd Rvkumr, 1992; Glor nd Zer, 1993; Bnerjee nd Newmn, 1993). Other uthors hve condtoned current utlty on offsprngs future ncomes (Becker nd Tomes, 1986) or consumpton (Mullgn, 1997, ch. 3). Here we tke the unconventonl route of condtonng current utlty on eductonl resources, whch n our context re worth somethng only when the chld s tlented.

22 372 D. Checch et l. / Journl of Publc Economcs 74 (1999) n # 1; c # h (1 2 t ). t t11 t11 t The tmng The lfe of ech person lsts for only two perods. A person born t dte t knows the hstory of ttempts to get n educton nd of successes nd flures of former members of hs dynsty. In the prvte school system, he lso knows the mount tht the fther hs devoted to hs educton; whle n the stte school system he knows the prevlng level of eductonl qulty of the system. On the bss of the hstory of hs dynsty he now computes hs belef on hs 39 t own tlent, denoted by n. He then decdes whether or not to go to school, choce whch s denoted s the choce between Y or n N respectvely. If he decdes Y, he lso decdes the mount of effort he devotes to the lernng ctvty. He then goes to school, nd ths s the end of the frst perod. At tme t 1 1 the tlent of the person s reveled nd ht11 s determned. In the stte school system the tx rte tt11 s then voted by the old generton. Then the remnng ncome s consumed nd txes re pd, or, n the prvte school system, the mount et11 of funds for the educton of the son s provded. Then the son s born nd the lfe of the older generton ends. Note tht, to smplfy notton, genertons do not overlp n ths model, but n ech clendr perod both genertons re lve: the oldest n the frst prt nd the youngest n the second prt of the perod. To summrse, nd to clrfy the nformtonl restrctons for the gents: the decson bout educton (tht s, whether to go to school, nd f so how much effort to spend n educton) s tken wthout knowledge of the tlent of the person; the vote on txes, the consumpton decson, nd the mount for the educton of the son, re decded fter the ddtonl nformton on the tlent of 40 the person hs been obtned Lernng bout tlent Consder person wth n ntl belef n n hs own tlent. If he decdes to go to school nd he s successful, he wll chnge to 1 the belef n hmself whle the 39 Note tht t the moment of decdng bout schoolng, ech person lerns bout hs tlent from hs fmly hstory, but not from hs performnce n the erly stges of hs educton. Ths s clerly n extreme ssumpton. We hve two resons to defend t. The frst s tht some of the mportnt decsons bout schoolng re tken t the very erly stges of the educton. For nstnce, the qulty of the elementry educton s mportnt, nd hs sometmes decsve nfluence on future choces. The second reson s tht we cn esly thnk of rcher model where, sy, ech gent mkes successve choces n educton, nd receves t ech step sgnl correlted wth hs tlent from hs performnce. Ths model would yeld the sme qulttve results s ours (provded, of course, tht these sgnls re not too precse). 40 For dscusson of the prdox of votng wthn ths frmework, see the CEPR WP verson of ths pper, n. 1466, October 1996.

23 D. Checch et l. / Journl of Publc Economcs 74 (1999) belef on the tlent of hs son wll be 1 2. After flure n school, nsted, these two belefs wll be, respectvely, 0 nd. If the person decdes not to go to school, then he wll gther no nformton bout hs own tlent nd wll hve belef ˆn ; 1 (1 2 2)n (4.4) n the tlent of the son. We denote by ˆ n the th terte of the functon defned n (4.4). Ths s functon ncresng n n, nd ts tertes converge to the vlue 1/2 41 ndependently of the ntl vlue. In prtculr, snce the belef of the frst member tht follows flure n school s n 5, ths functon tells us the belef of the th member of dynsty whch hs not ttempted schoolng fter the flure. Ths vlue, gven by the functon n 4.4 computed t n 5, s equl to 11 â ; 0.5(1 2 (1 2 2) ). (4.5) 4.7. The optml polces We begn wth the cse of the prvte school system. The optml polcy s decded by bckwrd nducton from the second perod, fter the decson between Y or N hs been tken (nd, n the cse of decson Y, the mount of lesure n t hs been chosen). In the second perod we hve therefore three possble cses: Y nd success, Y nd flure, nd N. In ech of these cses the problem of the gent s to mxmze for gven humn cptl ht11 nd belef nt11 on the tlent of the son: mx log c 1 n log e, subject to c 1 e # h (c t11,e t11) t11 t11 t11 t11 t11 t11 whch hs n optml e t11 equl to: nd vlue: n t11 ]]] h t n t11 (1 1 n ) log h 1 L(n ) t11 t11 t11 where the functon L s defned n Appendx B.1. So the optml expense n cse of Y decson nd success s et11 5 (1 2 )/ (1 1 (1 2 ))h t11; n the cse of Y nd flure we hve: et11 5 /(11 ); nd fnlly, f the decson hs been N, nd the belef on hs own tlent ws n, then: et11 5 n/(11 ˆ ˆ n ). In the cse of the stte system, the mportnt decson n the second perod s the 41 A relted lernng process s n Pketty (1995) lthough n tht model people lern bout prmeter tht s socl nd not dynstc.

24 374 D. Checch et l. / Journl of Publc Economcs 74 (1999) one bout votng, snce consumpton s pure resdul from ncome fter pyment of txes. The optml tx rte t s n t11 ]]]. 1 1 n t11 t11 So n the three cses correspondng to the one descrbed bove for the prvte system cse we hve: tt11 5 (1 2 )/(11 (1 2 )); tt11 5 /(11 ); nd tt11 5 n/(11 ˆ ˆ n ), respectvely. We cn now solve the problem of decdng n the frst perod the pr (Y, n t)(go to school, wth effort n ), versus N. Levng the detls to Appendx B.2, n order t to understnd the optml polces n the two systems t my be helpful to focus on three genertons, ech one lvng for two perods: the grndfther, born t t 2 1, the fther, born t t, who s the gent whose two perods decsons re beng 42 modelled, nd the son, born t t 1 1. In the prvte system the optml choce of expendture for educton of the fther s functon of the fther s belef on the son s tlent, nd of the fther s P t11 t11 t11 relsed humn cptl; we denote ths functon by e (n, h ). Furthermore, the fther s optml choce of Y versus N, nd of effort n school, s functon of the humn cptl of the grndfther nd of the vlble qulty of educton (decded by the grndfther); we denote ths functon, whch wll hve to be P t11 t t t postve for fther to go to school, by D (n, e, h ). Smlrly n the stte system, the optml fther s vote on txes s functon of S the fther s belef n the son s tlent; we denote ths functon wth t t11(n t11). Furthermore, the fthers s optml choce of Y versus N, nd of effort n school, s functon of the humn cptl of the grndfther nd of the verge qulty of S educton vlble to the fther n the stte system, e t. We denote ths functon, S S 43 whch wll hve to be postve for fther to go to school, by D t11(n t, e t, h t). P S S Both functons D t11(n t, e t, h t) nd D t11(n t, e t, h t) re crucl to determne moblty n the two systems. A detled dscusson of ths ssue, nd of the two functons, s developed n Secton The typcl hstory of dynsty To get some ntuton bout the wy n whch the model works we cn follow the typcl pth of dynsty. After flure n school of gven member, hs son wll hve belef n hs own tlent nd humn cptl equl to 1. Now for 42 Remember tht n ech clendr perod two genertons re lve, but they do not overlp: the oldest lves n the frst prt nd the youngest n the second prt of ech perod. 43 Note tht n generl the qulty of educton vlble to the fther depends on the ggregte humn cptl nd on the medn voter preferred tx rte n the generton of grndfthers, but n stedy stte t wll be dentcl for ll genertons.

25 D. Checch et l. / Journl of Publc Economcs 74 (1999) sequence of perods the members of the dynsty wll choose not to go to school becuse ther self confdence s too low. Durng these perods, however, the belef on tlent grows (by the fct tht the tertes of the updtng rule (4.5) re ncresng) untl t reches crtcl level t whch the correspondng member of the dynsty decdes to go to school. For convenence we shll denote ths crtcl level n * P n the prvte school system nd n * S n the stte school system cse. Ths crtcl level, or, equvlently, the length of ths ntl sequence of perods wll depend of course on the nsttutonl rrngement nd on the equlbrum; we dscuss lter how to chrcterse t, nd the vrous ddtonl fctors tht nfluence such crtcl level n the two systems. In cse of success n school nd untl new flure occurs (n whch cse the cycle we hve just descrbed strts ll over gn) the dynsty goes through sequence of ncresngly better perods. In ech of these perods the members go to school, cqure humn cptl n n ncresng quntty nd keep the belef to hgh level. In the prvte school system the members devote n ncresng mount of ncome to the educton of ther chldren; whle n the stte school system they vote for lrge tx rtes n support of educton. Eventully, however, flure occurs nd the cycle strts over Equlbr nd stedy stte dstrbutons In ths pper we shll concentrte our ttenton on the long run property of equlbr; nd they cn be esly studed by consderng the nvrnt dstrbuton on the relevnt vrbles: humn cptl, belefs over tlent, nvestment n educton nd so on. From our prevous dscusson of the typcl hstory of dynsty t should be cler tht only certn belefs over tlent re possble n the long run, for gven crtcl belef. Ech dynsty experences flure wth certnty over n nfnte tme horzon. After ths, the belef of the member of the dynsty n the next generton over hs own tlent t the moment of decdng bout hs schoolng effort s (.e. the probblty of beng dfferent from hs prent). The followng k members updte ther belefs ˆ, k 5 1,2,... usng (4.5) wthout gong to school untl the crtcl level s reched. At tht pont the correspondng member of the dynsty goes to school, tlent s reveled nd the belef cn only go bck to (n cse of flure n school) where the cycle begns gn, or to 1 2 (n cse of success); from ths lst belef the only trnstons possble re ether to 1 2 gn (success) or to (flure). If the crtcl level s bove 1/2 there re countbly mny belefs possble; f t s below, then there re only fntely mny. In both cses, however, they re 2 subset of the countble set h,, ˆ ˆ,..., 12 j. Note tht, n turn, ths wll produce countble set of possble humn cptl level, nd of possble expendtures n educton nd of tx rtes voted.

26 376 D. Checch et l. / Journl of Publc Economcs 74 (1999) In order to exmne the structure of the nvrnt dstrbuton, the frst step s the defnton of the pproprte stte spce: Defnton 4.1. The stte spce of the process s the product 3 H 5 [0, 1 1] 3 R of belefs over hh, Lj nd of humn cptl vlues. Ths stte spce hs to be understood s follows. For the pr (n, h), n s the belef of person n hs own tlent, t the moment n whch he decdes the schoolng effort n; nd h s the humn cptl tht the sme person hs t the end 44 of the schoolng perod. The followng Lemm descrbes formlly the trnston probbltes over ths stte spce: let be such tht the belef ˆ s the crtcl belef, n * or n *. Then: P S Lemm 4.2. The trnston probbltes 3 H re s follows (wp: wth probblty): k21 k from ( ˆ,1)to ( ˆ,1)for k 5 0,..., 2 1, wp 1; 21 from ( ˆ,1)to ( ˆ, h 0) wp ˆ, nd to ( ˆ,1)wp 1 2 ˆ ; from ( ˆ,1)nd (1 2, 1)to (, 1)wp 1; from ( ˆ, h 0) to (1 2, h 1) wp 1 2, nd to (1 2, 1)wp ; from (1 2, h j) to (1 2, h j11) wp 1 2, nd to (1 2, 1)wp. The bove trnston probbltes mply tht, fter flure nd f t does not go to school, dynsty moves wth certnty cross sttes chrcterzed by humn cptl equl to 1 nd by subsequent updtes of the belef n tlent. When the dynsty reches the crtcl level of self confdence t goes to school. Snce the ntl belef fter flure s correct, the updted belef on tlent s equl to the true probblty of beng tlented. Therefore, wth probblty ˆ the decson to go to school s successful nd h0 humn cptl s ccumulted; wth probblty 1 2 ˆ, nsted, the member of the dynsty s untlented nd humn cptl remns equl to 1. If the dynsty keeps beng successful no more updtng s needed becuse ech subsequent member knows he s the offsprng of tlented prent. Therefore, wth probblty 1 2 the dynsty contnues to be successful nd ccumulte ncresng humn cptl, whle wth probblty t fls, humn cptl flls to 1 nd the story strts ll over. The defnton nd the computton of the nvrnt dstrbuton for these trnston probbltes s reported n the Appendx B.3. We dscuss nsted, n the next secton, how the probbltes n the trnston mtrx, nd therefore ntergenertonl moblty, depend on the type of school system. 44 See the CEPR WP verson of ths pper (n. 1466, October 1996), for proof tht ths stte spce s suffcent descrpton of the process n the sense tht the fct tht dynsty s n stte x [ X t tme 0 provdes suffcent nformton to descrbe the future condtons of the dynsty.

27 D. Checch et l. / Journl of Publc Economcs 74 (1999) Moblty As we hve seen, even on the reduced stte 3 H the trnston mtrces re nfnte: so we hve to fnd some smple ndex of the dfferent degrees of moblty n the two eductonl systems. The smplest s the trnston probblty mong two dfferent clsses of humn cptl. We dvde the totl populton n two clsses: those who hve humn cptl equl to 1, the mnmum vlue, nd those who hve hgher vlue. The frst clss wll be denoted by C 1, the second by C 2. We cn then compute the trnston mtrx between these two clsses, sy p j, 5 1, 2; j 5 1, 2, where pj s the probblty tht dynsty trnsts from C to C j; we hve tht: Lemm 5.1. The mtrx of trnston probblty cross clsses s: S D ˆ ˆ 1 2]] ]] (1 2 ) The term ˆ / 1 1 s decresng functon of. The proof s n Appendx B.4. Note tht ˆ /( 1 1) 5 when 5 0. The vlue of ˆ /( 1 1) cn be consdered n ndex of moblty t the stedy stte equlbrum of the system: the hgher ths vlue the more moble the socety s. Note tht t s nversely relted to the nteger, the number of perods dynsty remns dscourged fter flure. We summrse ths s our defnton of moblty: Defnton 5.1. A socety s more moble, the shorter the perod n whch dscourged dynsty does not ttempt to cqure educton; tht s, the lower the vlue of the crtcl (.e. the lower the level of self-confdence needed to go to school). We now turn to dscusson of ths crtcl vlue nd of how t s nfluenced by the nsttutonl settng for educton fnncng Why does moblty dffer n the two nsttutonl settngs? The crtcl vlue of s the frst tme fter flure tht the expected utlty from Y decson s hgher thn the expected utlty of n N decson. In the prvte school system, for fther wth belef n n hs own tlent nd vlble qulty of

28 378 D. Checch et l. / Journl of Publc Economcs 74 (1999) educton e, the dfference between these two expected utltes s gven by the 45 functon: p 1 D (n, e) ; nb[1 1 (1 2 )]LS]]]]] nb[1 1 (1 2 )] D s g 1 n[1 1 (1 2 )]log(ue ) 1V(n) 5 (5.6) g mx logn 1 n[1 1 (1 2 )]log[ue (1 2 n) ]1V(n) (5.7) n[[0,1] where the term V(n) s equl to: V(n) ; nl(1 2 ) 1 (1 2 n)l() 2 L(n ˆ ). (5.8) nd the functon L s defned n Appendx B.1. In the stte school system, for the fther wth belef n on hs own tlent nd vlble qulty of educton e, the dfference between the expected utltes of the Y nd N decsons s gven by the functon: SD s 1 g D (n, e) ; nbl ] 1 n log(ue ) 5 (5.9) nb g b mx logn 1 n log[u(th) (12 n) ]. (5.10) n[[0,1] Moblty under the two systems dffers whenever, everythng else beng equl, p the frst crtcl generton for whch D becomes postve s dfferent from the s frst crtcl generton for whch D becomes postve. It s, therefore, crucl to consder how the two functons dffer for ech gven. One mportnt dfference s tht stte school system trnsfers revenues from hgh ncome fmles to low ncome fmles nd mkes better educton vlble to the ltter t no ddtonl cost. Ths effect of stte system, whch we lbel trnsfer of resources, s commonly quoted s the mn reson for whch publc educton should rse ntergenertonl moblty. But other fctors, hghlghted by our frmework, pont n the opposte drecton mkng t possble for prvte system to nduce more moblty. Frst fther n the prvte system who decdes hs effort n the producton of hs own humn cptl lso tkes nto ccount the fct tht n cse of success the hgher ncome vlble to hm wll lso postvely ffect hs son. In the stte system nsted hgher ncome wll not hve ths effect, snce the expense n educton comes from common fund, nd the contrbuton of ech person to t s neglgble. Everythng else beng equl, ths mkes the vlue of the Y choce hgher n the prvte system, b d 45 Ths s the functon tht ws ntroduced n the secton n whch optml frst perod polces were descrbed. Here the humn cptl of the grndfther does not pper s n rgument of the functon p s D, nd nlogously for D below, becuse t s equl to 1 for the crtcl generton.

29 D. Checch et l. / Journl of Publc Economcs 74 (1999) s reflected by the coeffcent n[1 1 (1 2 )] rther thn n n front of loght11 n the two expressons (5.7) nd (5.10); nd t ncreses the effort spent on educton n the stte system (s s cler from the Eqs. (B.14) nd (B.17) n the ppendx). We cll ths fctor effectve ltrusm. Furthermore, for gven, the medn tx rte n the stte system s dfferent from the preferred tx rte ccordng to whch the crtcl prent would lke to fnnce educton for hs son. In generl the ltter s lrger thn the former nd ths fctor, whch we lbel rte of expendture, tends to reduce the trnsfer of resources 46 fctor nd the cpcty of stte system to ncrese moblty. Fnlly, the fct tht n the stte system the tx rte s unque mkes ny nformton tht person my cqure on hs nd hs son s personl bltes useless, becuse he cnnot djust the expense n educton for the son ccordng to ths nformton. Formlly ths effect cn be relted to the presence of the term p s V(n) n the expresson for D ; ths term s bsent, nsted, n the expresson for D becuse n the stte system the tx rtes n the three events Y nd success, Y nd flure, nd N re the sme. The opposte s true for fther n the prvte system p s reflected n the term V(n) n the expresson for D. We my cll ths term the vlue of nformton, whch s due to the nformton cqured by gong to school versus not gong. If he goes to school, the fther wll know f hs tlent s hgh or low: hence he wll know f the tlent of the son s more lkely to be hgh (wth probblty 1 2 ) or more lkely to be low (wth probblty ). If he does not go, he wll only hve the nformton contned n hs updted belef n. ˆ But the functon L n Eq. (5.8) s convex; so we conclude tht the vlue of nformton s lwys non-negtve nd therefore ncreses the desrblty of humn cptl nvestment n the prvte system. We cn now summrse our comprson of the two functons D nd D,.e. of the fctors tht determne the crtcl decson to cqure humn cptl n the two systems. We hve seen four fctors tht ffect ths crtcl decson. Three of them, the effectve ltrusm, the rte of expendture nd the vlue of nformton, tend to mke the prvte school system more moble. The frst mkes hgher ncome even more ttrctve for the fther n the prvte system, thnks to the drect postve effect on the son. The second nduces lower moblty n the stte system by forcng common lower tx rte, chosen by the medn voter, on the crtcl voter. The thrd smply dds n the prvte system n ddtonl reson to go to school: cqurng nformton on tlent. On the other sde there s the trnsfer of resources fctor. Ths fctor cptures p s 46 To see why, let s cll the crtcl voter the voter n the stte system whose son s the frst gent to go to school. We cn compre hs poston to the poston of the medn voter. Observe tht the proporton of unsklled ndvduls s lrger thn hlf when ± 0. (The proof of ths sttement s n Appendx B.4.) Then the medn voter s lwys unsklled f ± 0; s result the tx rte for the medn voter s lwys lower thn the optml tx rte for the crtcl voter.

30 380 D. Checch et l. / Journl of Publc Economcs 74 (1999) the fct tht txton n stte systems trnsfers revenues from hgher to lower ncome dynstes, ncresng the qulty of educton vlble to the ltter. In the next secton, wth the help of numercl computtons, we explore whch condtons renforce the dfferent set of fctors outlned bove, mkng ntergenertonl moblty hgher under one or the other stylsed educton system. 6. Numercl computtons We use the model descrbed bove to generte numerclly two prdgmtc cses: one n whch centrlsed nd egltrn educton system nduces more moblty nd one n whch the opposte s true. Both outcomes re possble 47 dependng on prmeter vlues. In Tble 13 we present the relevnt ndctors tht descrbe the performnce of ech educton system n the two dfferent prdgmtc cses. In both these cses the prmeter, whch mesures the persstence n the trnsmsson of tlent, hs been set equl to 0.1 whle the scle prmeter u n the producton functon of humn cptl hs been set equl to 2.8. The two prdgmtc cses dffer nsted for the vlues of the prmeters b nd g. These prmeters mesure, respectvely, the elstcty of humn cptl ccumulton wth respect to effort (1 2 n t) nd wth respect to the vlble qulty of educton e t. Prt A of Tble 13 shows tht the mn results of Glomm nd Rvkumr (1992) hold lso n our model. In both Cse 1 nd Cse 2, the stte system fetures lower degree of nequlty but lso lower totl humn cptl (.e. lower ncome) nd lower totl expendture n educton. The medn ncome n the upper clss, tht s mesure of nequlty becuse ncome n the lower clss s equl to 1 for everybody, s n fct lrger n the prvte system ndependently from g nd b. The counterprt of ths greter nequlty s the lrger ccumulton of humn cptl nd the lrger expendture n educton tht the prvte system cn generte, thnks to the fct tht fthers re free to spend wht they prefer for the educton of ther sons on the bss of ther ncome nd ther belefs on tlent. In the stte system, nsted, where the totl qulty of educton s determned by the common tx rte decded by the medn voter nd by the ggregte mount of humn cptl, the totl expendture n educton s lower. A common rgument n defence of publc schools s tht they offer better qulty of educton to poor dynstes tht, n prvte system, would otherwse spend too lttle for the educton of ther chldren. The lst column of Prt A n Tble 13 confrms ths ntuton: the crtcl expendture n educton e t, reported For the procedure followed n these numercl computtons see Appendces B.5 nd B Note tht mples tht the tlent of the son s ndependent of the tlent of the fther; therefore mples reltvely hgh nhertblty of tlent. We wll menton lter how the results chnge n relton to the vlues of nd u.

31 D. Checch et l. / Journl of Publc Economcs 74 (1999) Tble 13 Stedy stte performnce ndctors of the two systems b g School Tx Medn Totl Totl Crtcl system rte ncome humn expendture expendture upp. clss cptl n educton n educton Prt A Cse Stte Prvte Cse Stte Prvte Prt B Proporton Probblty Crtcl Genertons of of upwrd belef wthout school unsklled moblty fter flure Cse Stte Prvte Cse Stte Prvte All the ndctors re computed t the stedy stte for: nd u The medn ncome of the upper clss s mesure of nequlty n these economes gven tht ll the ndvduls n the lower clss hve n ncome equl to 1. Totl humn cptl s defned s n Eq. (4.1). Totl expendture n educton s the sum of wht ech fther spends for the educton of hs son n the prvte system, whle n the stte system s gven by Defnton B.2. The crtcl expendture n educton s the educton vlble to the generton tht goes to school: t s equl to totl expendture n the stte system becuse of the normlzton of populton. The proporton of unsklled s equl to p(11 ) s n Secton B.3. The probblty of upwrd moblty s equl to the term ˆ /( 1 1) n Lemm 5.1. The crtcl belefs re the belefs n * or n * P S, respectvely, for the prvte nd the stte system, tht dynstes hve to rech fter hstory of no schoolng n order to decde to mke n nvestment n educton. The frst generton n school fter flure s the vlue of the crtcl s chrcterzed, for exmple, n Lemm 4.2. n ths column, s wht the fthers of the frst generton gong to school spend for the educton of ther chldren. Tble 13 shows tht n both Cse 1 nd Cse 2 the stte system offers better qulty of educton to ths crtcl generton nd ths s n mplcton of the trnsfer of resources fctor tht we mentoned n the prevous secton. The reder wll recll tht ths s ndeed the fctor tht tends to 49 fvour moblty n stte system. However, the reder wll lso recll tht other fctors pont n the opposte drecton. Prt B of Tble 13 shows ndeed tht the provson of better qulty of educton to poor fmles does not necessrly mke the stte system more moble thn the prvte system. The prdgmtc cse n whch the stte system fls to generte more moblty s Cse 1 n whch b nd g Tble 13 shows 49 Note tht gven tht the populton s normlsed to 1, the totl expendture n educton n the stte system s equl to the expendture for ech ndvdul ncludng the crtcl one.

32 382 D. Checch et l. / Journl of Publc Economcs 74 (1999) tht n ths cse the probblty of upwrd moblty s hgher n the prvte system (0.09) thn n the stte system (0.05). A greter level of self confdence (.e. the crtcl belef) s needed n the stte system n order to go to school (0.42 versus 0.18) nd seven genertons (nsted of one n the prvte system) wt fter flure wthout gong to school before self confdence becomes suffcently hgh to try the humn cptl nvestment. In ths cse the publc offer of equl eductonl opportuntes s not suffcent to ensure more socl moblty becuse the reltve weght g of the qulty of educton n the producton functon for humn cptl s too low. As result the trnsfer of resources effect, whch tends to ncrese moblty n stte system, s domnted by the other three fctors, mentoned n the prevous secton, tht tend to ncrese moblty n prvte system: effectve ltrusm, the rte of expendture nd the vlue of nformton. On the contrry, n Cse 2, when b nd g 5 0.6, the qulty of educton s so mportnt for the ccumulton of humn cptl tht the stte system s cpble of nducng greter moblty: the reson s tht ths s precsely the stuton n whch the publc offer of better educton to poor fmles mkes the nvestment n humn cptl convenent. Incresng the vlues of the prmeters nd u (tht s, mkng the trnsmsson of tlent more rndom nd ncresng everythng else beng equl, the ccumulton of humn cptl n cse of success n school) mkes moblty more lkely n both systems but does not chnge ther qulttve reltve performnce n relton to the vlues of b nd g. Ths s cler from our chrcterston of the moblty mtrx n Secton 5: when the tlent of the chld s ndependent of the tlent of the prent, ths mtrx hs dentcl rows, rrespectve of the vlues of the prmeters nd of the schoolng system. To summrse the results of our numercl computtons, n order for the trnsfer of the resources fctor to prevl, mkng the stte system more moble, two mn condtons hve to be met. Frst, redstrbuton of eductonl resources from rch to poor dynstes hs to be hgh enough to ensure suffcently better qulty of educton for poor dynstes; nd ths s the common rgument supportng the de tht stte systems should generte more upwrd moblty. And second, the eductonl process must be such tht ndvdul effort s reltvely less mportnt thn the qulty of educton for successful ccumulton of humn cptl. 7. Conclusons If one of the gols of publc educton system s to fvour equl opportuntes of socl moblty, the Itln school system fled to cheve ths gol. The centrlsed nd publc structure of educton fnncng n Itly hs ndeed ensured substntl unformty of the quntty nd qulty of educton offered to both rch nd poor fmles; but despte ths offer of equl opportuntes Itly, n

33 D. Checch et l. / Journl of Publc Economcs 74 (1999) comprson to the US, dsplys lower ntergenertonl moblty not only n terms of occuptons but lso n terms of educton levels. The flure of the Itln publc system s certnly not flure of publc educton per se. Germny, for exmple, where educton s mnly publc, hs 50 recently been shown to feture hgher ntergenertonl moblty thn the US. Note, however, tht the Germn stte school system s hghly selectve nd dversfed, n prtculr t the hgher levels. Indeed, n ndcton of our model s tht unverstes represent the level t whch t s rsky to offer publc educton n unform nd egltrn wy becuse such n offer my decrese the ncentve of poor fmles to nvest n the ccumulton of humn cptl even f educton s free. Prmry educton, on the contrry, s the level t whch ndvdul effort s reltvely less mportnt thn the qulty of schools n the eductonl process, nd stte school system certnly genertes the condtons for lrger humn cptl nvestment of poor fmles. Our comprson between Itly nd the US lso suggests tht decentrlzed nd non-stndrdzed school system llows better tlorng of the vlble eductonl opportuntes to the needs of the demnd nd supply of lbor. Everythng else beng equl, the possblty to choose mong lrger vrety of nvestment opportuntes should ncrese the ttrctveness of n nvestment n humn cptl. Any form of consultng or screenng cpble of helpng the chldren of dsdvntged fmles to cqure more nformton on ther tlents nd tttudes should mprove ther cpcty to mke the best schoolng decsons. To conclude, n world n whch fmly bckground s mportnt for lbor mrket success, n excessvely centrlzed nd unform qulty of educton, prtculrly t the unversty level, does not necessrly help poor chldren nd my tke wy from them fundmentl tool to prove ther tlent nd to compete wth rch chldren. Acknowledgements We would lke to thnk the nonymous referees, Dron Acemoglu, Anthony Atknson, Rolnd Benbou, Guseppe Bertol, Alex Cukermn, Frnços Bourgugnon, Ronld Dore, Rchrd Freemn, Lrry Ktz, Thoms Pketty nd semnr prtcpnts t IGIER, CORE, NBER, EUI, IIES, Bnk of Itly, Unverstes of Moden, Sen, Npol, Prm, Ctholc n Mln nd Tlburg, for ther nsghtful comments on prevous versons of ths pper; Bob Revlle, Antono DeLllo nd the Bnk of Itly for provdng us wth the dt; Govnn Oppenhem nd Rffele Tngorr for excellent reserch ssstntshp; Confndustr nd CNR (grnts N CT10 nd CT10) for fundng. Andre Ichno 50 See Checch (1997) nd Couch nd Dunn (1997).

34 384 D. Checch et l. / Journl of Publc Economcs 74 (1999) grtefully cknowledges the hosptlty of CES, Munch, nd IIES, Stockholm where he resded whle workng on ths pper. All errors re our own. Appendx A. Emprcl ppendx The Itln dt come from ntonl survey conducted n 1985: the Indgne Nzonle sull Moblt Socle. A representtve smple of 5016 ndvduls ged between 18 nd 65 ws ntervewed on ther workng lfe, ther socl tttudes nd ther fmly bckground. From ths fle, we extrcted nformton concernng the sttus of the respondent n 1985 nd hs/her fmly when he/she ws 14. Therefore, whle respondents re observed n the sme yer (1985), ther prents re observed n dfferent yers, rngng n prncple from 1934 to From the orgnl smple we excluded ll ndvduls not belongng to the lbor force or whose occupton ws unknown. In ddton, for comprson wth the US smple (see below), we excluded ll women nd ll ndvduls younger thn 25; ths ltter restrcton s justfed by the fct tht we wnt to llow for the possblty of completng unversty currcul. Wth these restrctons the orgnl smple reduces to 1666 son fther couples; ther ge dstrbuton s reported n Tble 12. US dt comes, nsted, from the Pnel Study of Income Dynmcs (PSID), whch conssts of longtudnl smple of fmles ntervewed for the frst tme n 1968 nd then followed on yerly bss. The subsmple tht we use s n extrct of the orgnl smple contnng nformton on 1050 fther son couples, whose occupton ws known nd whose ge ws greter thn 25 t the tme of the ntervew. An mportnt dfference between the two dtsets s tht US dt re bsed on drect ntervews wth both sons nd fthers, whle Itln dt on fthers re bsed on sons recollectons. Informton on US sons ws collected n 1990, whle nformton on correspondng fthers refers to Becuse of the short ntervl between the two ntervews, US sons re on verge consderbly younger thn ther fthers, s shown n Tble 12. In ech country we consder the medn ncome pd by ech occupton s the ndctor of ndvdul long term economc sttus. We hve not found sngle clssfcton of elementry occuptons pplcble to both countres, nor converson tble from the ntonl clssfctons nto common nterntonl one. For Itly our dtset s bsed on the occupton clssfcton developed by DeLllo nd Schzzerotto (1985), who grouped 13,000 elementry occuptons nto 97 bsc groups, chrctersed by smlr degree of socl desrblty (s mesured by the rnkng obtned n smple ntervews). For the US, we rely on the clssfcton scheme developed by Duncn (1961). In ths cse the clssfcton scheme ncludes 96 bsc groups. As fr s occuptonl medn ncomes re concerned, for the US smple we hve nformton bout the ernngs of both genertons. On the contrry, n the

35 D. Checch et l. / Journl of Publc Economcs 74 (1999) Itln smple, we do not hve ny drect nformton bout ncomes. We therefore merged occuptonl ncome dt from nother source ccordng to the followng procedure. We strted wth ncomes tken from the 1987 wve of the Indgne su Blnc delle Fmgle Itlne run by the Bnk of Itly. Snce ths survey reports net ncomes, we hve estmted the correspondng gross ncomes on the bss of 51 the relevnt fscl legslton for We then estmted n ernngs functon usng gross ncomes. Regressors n the ernng functon were: ge, sx educton dummes, nne qulfcton dummes, 11 sector dummes nd fve geogrphc dummes. We used the estmted prmeters to predct ncomes for the ndvduls n our mn smple. From these predcted ndvdul ncomes we constructed the occuptonl rnkng bsed on the medn ncome of ech occupton. Ths procedure could of course be used only for the generton of sons. Therefore we were forced to use lso for fthers the occuptonl rnkng constructed for sons. In order to llow for menngful comprson, we mposed the sme restrcton on the US dtset s well. But n ths dtset we hve been ble to check tht the rnkng of occuptons n terms of medn ncomes s frly stble cross genertons: the correlton between occuptonl ncomes constructed on the dstrbuton of sons nd on the dstrbuton of fthers s equl to Appendx B. Theoretcl ppendx B.1. A useful functon The followng optmzton problem ppers repetedly n our pper: mx log(x 2 y) 1 z log y. y[[0,x] Its soluton s y 5 (z/(11 z))x, nd the vlue s: (1 1 z) log x 1 L(z), (B.1) where we hve denoted: L(z) ; z log z 2 (1 1 z) log (1 1 z). (B.2) In order to lghten the presentton, we often refer to ths functon n the pper. 51 The Itln system of personl ncome txton s step-wse progressve nd llows for tx deductons bsed on household composton. It s therefore possble to reconstruct for ech ndvdul hs/ her gross ncome strtng from hs/ her net ncome. Note tht prelmnry versons of ths pper hve crculted wth evdence bsed on net ncomes.

36 386 D. Checch et l. / Journl of Publc Economcs 74 (1999) B.2. Frst perod optml polces We begn wth the prvte school system. The gent born t t s comprng the mxmum between two qunttes. The frst s the expected mxmum utlty from the choce (Y, n ) tody, ssumng tht n the followng perod the gent wll mke t the optml choce (of consumpton nd expendture on educton for the son) condtonl on the new nformton bout hs own nd the son s tlent. Wth belef nt on hs own tlent the frst choce gves success wth probblty nt nd flure wth probblty 1 2 n. If we substtute the vlues of the second perod n the t utlty functon (4.2) nd wrte the mxmston problem for the frst perod we get: mx log n 1 n s[1 1 (1 2 )] log h 1 L(1 2 ) d1 (1 2 n )L() (B.3) n [[0,1] t t t t11 t The optml choce of lesure s 1 ]]]]]] (B.4) 1 1 nb[1 1 (1 2 )] nd the vlue s S D 1 g d nb[1 1 (1 2 )]L ]]]]] 1 n[1 1 (1 2 )] log(ue h) 1 nl(1 2 nb[1 1 (1 2 )] ) 1 (1 2 n)l(). (B.5) The second quntty we need to consder s the expected mxmum utlty from choce N tody. The effort does not ffect the humn cptl, so the optml choce of lesure s 1; the belef on the son wll be ˆ n t, nd the correspondng vlue hs the very smple form: L(n ) 5 L(n ˆ ) (B.6) t11 t The resonng n the cse of the stte school system s smlr. The gent solves: mx logn 1 n s(1 2 t) log h 1 (1 2 ) log(th) d1 (1 2 n ) slog(1 2 t) 1 n [[0,1] t log(th)d t t t11 t where the tx rte t s the prevlng tx rte (nd not the tx rte chosen n the second perod by the gent). The optml choce of lesure s 1 ]] 1 1 nb (B.7) nd the vlue s

37 D. Checch et l. / Journl of Publc Economcs 74 (1999) g nblsd ] 1 n log(ue ) 1 log(1 2 t) 1 [(1 2 )n 1 (1 2 n)l()]log(th). nb B.3. The nvrnt dstrbuton (B.8) In ths secton we provde the vlues of the nvrnt dstrbuton over the stte 3 H, for gven vlue ˆ of the crtcl belef. We denote by P, respectvely S, the trnston mtrx n the prvte, respectvely stte, system; P(x, x9) s the probblty of the trnston from x to x9. An equlbrum nvrnt dstrbuton s probblty F* tht reproduces tself, when ech person mkes the optml choce. More formlly we sy: Defnton B.1. A stedy stte equlbrum dstrbuton for the prvte school system s probblty mesure F * over the product 3 H such tht P () F * P 5 F * PP, () ech member of ech dynsty s choosng effort nd school expendture P P optmlly, ccordng to the functons (D, e ) of Secton 4. Smlrly we sy: Defnton B.2. A stedy stte equlbrum dstrbuton for the stte school system s trple (t*, e*, F * S ) of tx rte, n verge educton qulty nd probblty mesure F * S over the product spce of belefs nd humn cptl such tht (FS,H s the mrgnl of FS over H): () F * S 5 F * S S; () t* ehdf * S,H (h) 5 e*; () t* s the medn voter tx rte for F * S ; (v) ech member of ech dynsty s choosng effort nd votes on tx rte S S optmlly, ccordng to the functons (D, t ) of Secton 4. The nteger s the only fctor determnng ths dstrbuton. Therefore, n n nvrnt dstrbuton, for ech nteger k 5 0,1,..., 2 1 there s correspondng k frcton pk of the populton n stte ( ˆ, 1), frcton p 21(1 2 ˆ ) n stte ( ˆ, 1), nd frcton p ˆ n stte ( ˆ, h 0). It s mmedte from the trnston mtrx tht: p 5 p???5p ; p. (B.9) It wll be useful now to use the followng nottonl devce: the stte (1 2, 1) j

38 388 D. Checch et l. / Journl of Publc Economcs 74 (1999) s the stte of person wth belef (1 2 ) n the frst perod of hs lfe, comng fter j consecutve successes n hs dynsty, nd who fls t school. Now denote by qj nd rj respectvely the frcton of the populton n stte (1 2, h j) nd (1 2, 1 j) we hve: q 5 p ˆ ; p ˆ ; r 5 p (1 2 ˆ ) ; p(1 2 ˆ ); (B.10) q 5 (1 2 )q, r 5 q, j 5 0,1,2,... (B.11) j11 j j11 j But now observng tht: ` p 5O r j j50 we my wrte: but lso: p 1???1p 1O r 5 ( 1 1)p 0 21 j j50 p 1???1p 1O r 1O q j j j50 j50 nd lso from (B.11) ` q O 0 q j 5] j50 Usng the equtons bove we get: 1 p(1 1 ) 1] q0 5 1, whch we cn solve to get fnlly: ` ` ` ˆ ˆ p 5 ]]]] ; q0 5 ]]]] ; q 5 ]]]], (B.12) ( 1 1) 1 ˆ ( 1 1) 1 ˆ ( 1 1) 1 ˆ ` 0 j where q 5 o (q ) s the frcton of the populton wth humn cptl greter thn 1 nd ( 1 1)p s the frcton of the populton wth humn cptl equl to 1. B.4. Proofs Proof of Lemm 5.1. Let F be n nvrnt dstrbuton for the process descrbed by the mtrx G. From the ergodc theorem, the mesure of the set of dynsty hstores wth two consecutve vlues of 1 of humn cptl s gven by:

39 D. Checch et l. / Journl of Publc Economcs 74 (1999) O F(n, h) S O G((n, h), (n9,h9)) D. h(n,h):h51j h(n 9,h9):h951j From our computton of the nvrnt dstrbuton we derve tht the bove quntty s equl to: p( 1 1) 2 2pˆ 1 q; whle the totl frcton of populton wth humn cptl 1 s p( 1 1). Tkng rtos nd usng the vlue for p nd q n the Appendx B.3 we get the result. The proof for the other row s obvous. 11 Recll now tht ˆ 5 0.5[1 2 (1 2 2) ]; clculus ppled to the functon x 21 (12(12 2) )x proves the second clm. Proof tht the proporton of unsklled ndvduls s lrger thn hlf when ± 0 (see footnote 46). The sttement s equvlent to ( 1 1)p. 1/2 whch n turn s equvlent to: â ]]], 1. ( 1 1) But ˆ 5 1/2[1 2 (1 2 2) 11 ]; so ths s equvlent to: 11 (1 2 2) ( 1 1); (B.13) Cll 2 5 x nd n to smplfy; nd observe tht n f(x) ; (1 2 x) hs dervtve t zero equl to (2n), nd s strongly convex. Then snce f(x). f(0) 1 f 9(0)x for every strongly convex functon, nd the bove expresson s exctly (B.13). B.5. Procedure for the numercl computtons In ths ppendx we descrbe the procedure to compute the long run equlbrum. We begn wth the prvte school system. The procedure checks for ech nteger f the correspondng belef ˆ s the crtcl belef of n equlbrum dstrbuton. Recll tht crtcl belef s the lest belef such tht the member of dynsty wth tht belef decdes to go to school. In the prevous secton we hve determned the stedy stte equlbrum proporton of the populton for the dfferent belefs. Note tht there re severl types of people hvng the belef 1 2 ; nmely, those whose dynsty hs hd sequence of one, two, nd so on successes. These types wll hve dfferent levels of humn cptl. We now proceed to determne these levels nd the correspondng proportons. Let us begn wth the frst. After the crtcl level ˆ s reched, the member of the dynsty goes to school. The fther hd humn cptl equl to 1,

40 390 D. Checch et l. / Journl of Publc Economcs 74 (1999) (21) belef n hs own tlent equl to ˆ, nd hs nvested e 5 ˆ /(11 ˆ )nthe educton of hs son. The son nvests the optml mount of effort gven these chrcterstcs, nd succeeds wth probblty ˆ. If he does, he hs humn cptl of S b b[1 ˆ 1 (1 2 )] ˆ h0 5u ]]]]]] ]]. 1 1 b[1 ˆ 1 (1 2 )] 1 1 ˆ D S Smlr rguments gve tht the dynstes wth j consecutve successes n the pst hve level of humn cptl tht follows the dfference equton S DS D b g (1 2 )b[1 1 (1 2 )] (1 2 ) (g 1d ) hj21 hj 5u ]]]]]]]] ]]]] 1 1 (1 2 )b[1 1 (1 2 )] 1 1 (1 2 ) for j 5 1,... We hve conjectured so fr tht the nteger determnes crtcl belef ˆ. The lst step of the procedure s to verfy ths conjecture. If t s true, we hve found stedy stte equlbrum; f t s not, we proceed to the next nteger. To verfy the conjecture we hve to check tht the belef ˆ s ndeed the lest one for whch people go to school. But the dfference n expected utlty between the two choces Y nd N for person wth belef n n hs own tlent, expendture e decded by the p fther nd humn cptl 1 of the fther s gven by the functon D. The fnl step s now obvous: fnd the lest nteger such tht S p â D ˆ,]] $ ˆ D The procedure to determne the stedy stte equlbrum for the stte school system s smlr, nd we provde here the mn lnes. In ths cse too we check f â s the crtcl belef of the equlbrum, for every. Recll now tht the preferred level of txes only depends on the belef of the fther t the moment of votng. A smple computton now determnes the medn voter n ths populton, nd the wnnng tx rte t( ˆ ). Also rguments lke the one gven bove gve the humn cptl for genertons wth j successes. The equtons re now: nd S âb g h0 5u ]]] e ; 1 1 ˆ b S D b D b (1 2 )b g d j21 hj5u ]]]] eh, 1 1 (1 2 )b for j 5 1,...Thee n the formuls for humn cptl bove s for the moment prmeter to be determned. Tkng nto ccount tht the proporton of populton j wth h s p ˆ, nd the proporton of populton wth h s q(1 2 ) for every 0 j D g

41 D. Checch et l. / Journl of Publc Economcs 74 (1999) j. 0 we cn now determne the ggregte humn cptl nd therefore the ggregte ncome, ths lst s functon of e (besdes ), H(, e) sy. Now solvng for e n e 5 t( ˆ )H(, e) determnes vlue of the educton qulty level n the stte school system e(), sy. The fnl step s, s before, the determnton of the nteger for whch ndeed the belef ˆ s the crtcl level. The functon gvng the dfference between the expected utlty of the Y nd the N decson, for person whose fther hs s humn cptl equl to 1 s now gven by: the functon D, nd s before we s conclude by determnng the lest nteger such tht D ( ˆ, e()) $ 0. B.6. A borderlne cse The support of the nvrnt dstrbuton s countble set. In the computton of the medn voter we begn to dd from the lower tx rte, ddng t ech step dscrete qunttes correspondng to the dfferent types of voters. It my hppen therefore tht one of these sums corresponds exctly to hlf of the voters. Ths s typclly n unlkely event; there s one cse however tht s prtculrly mportnt, nd requres detled dscusson. Suppose tht the crtcl,.e. the frst tme fter flure n whch dynsty tres to go to school, s zero. In the nvrnt dstrbuton exctly hlf of the populton would be unsklled, wth preferred tx rte equl to /(11 ), nd exctly hlf would be sklled, wth most preferred tx rte equl to (1 2 )/(11 (1 2 )). In ths cse the equlbrum n votng does not exst. In the numercl computtons, we present however the results for the cse n whch the crtcl s zero, nd the tx rte s equl to (1 2 )/(11 (1 2 )). We thnk the vlues we present re sgnfcnt for the followng reson. Consder n economy n whch the vlue of the prmeters re such tht wth 5 0 exctly hlf of the populton prefers the tx rte (1 2 )/(11 (1 2 )) to the rte /(11 ). Ths s not, t the correspondng sttonry dstrbuton, n equlbrum, becuse the proporton of populton votng for the hgher tx rte s not strctly lrger thn hlf. Consder however pth where the proporton of the populton wth humn cptl hgher thn 1 s lrger thn hlf, sy m 0. Along the pth the vlues of ggregte humn cptl nd the dstrbuton of humn cptl nd belef converge to the vlues of n economy wth tx rte equl to (1 2 )/ (1 1 (1 2 )). The trnston s the one descrbed n the prevous Lemm 5.1; so n the frcton of the populton wth belef hgher or equl to 1 2 s equl to ˆ m 0 n perod n, proporton strctly lrger thn hlf. So long ny such pth, n every perod, the economy s n n equlbrum n whch the vlues of verge humn cptl, ts dstrbuton mong the populton,

42 392 D. Checch et l. / Journl of Publc Economcs 74 (1999) nd so on re close to the vlues tht we report for the cse of the crtcl equl to 0, nd tx rte equl to (1 2 )/(11 (1 2 )). References Atknson, A.B., On ntergenertonl ncome moblty n Brtn. Journl of Post-Keynesn Economcs III (2), Atknson, A.B., Mynrd, A.K., Trnder, C.G., Report On the Rowntree Study, London School of Economcs, London. Atknson, A.B., The mesurement of economc moblty. In: Atknson, A.B. (Ed.), Socl Justce nd Publc Polcy, Whetshef Books, London, Chpter 4. Bnerjee, A., Newmn, A., Occuptonl choce nd the process of development. Journl of Poltcl Economy 101 (2), Brtholomew, D.J., In: 2nd ed, Stochstc Models for Socl Scences, Wley, London. Becker, G., Tomes, N., Humn cptl nd the rse nd fll of fmles. Journl of Lbor Economcs 4, S1 S39. Benbou, R., Heterogenety, strtfcton nd growth: mcroeconomc mplctons of communty structure nd school fnnce. Amercn Economc Revew 86, Benbou, R., 1996b. Equty nd effcency n humn cptl nvestment: the locl connecton. Revew of Economc Studes 63, Bbby, J., Methods of mesurng moblty. Qulty nd Quntty 9, Boudon, R., Mthemtcl Structures of Socl Moblty, Elsever, Amsterdm. Bowles, S., Gnts, H., Schoolng n Cptlst Amerc, Routledge nd Kegn, London. Brndoln, A., A Brd s-eye Vew of Long-run Chnges n Income Inequlty, Bnk of Itly, Mmeo. Checch, D., Educton nd ntergenertonl moblty n occuptons. Amercn Journl of Economcs nd Socology 4, Coblt, A., Schzzerotto, A., L moblt` socle n Itl, Il Mulno, Bologn. Conlsk, J., Rnkng moblty mtrces. Economcs Letters 29, Conlsk, J., Monotone moblty mtrces. Journl of Mthemtcl Socology 15, Couch, K., Dunn, T., Intergenertonl correltons n lbor mrket sttus: comprson of the Unted Sttes nd Germny. Journl of Humn Resources 32 (1), Cowell, F., Schluster, C., Mesurng Income Moblty wth Drty Dt. London School of Economcs, CASE Pper n. 16. Drdnon, V., Mesurng socl moblty. Journl of Economc Theory 61, DeLllo, A., Schzzerotto, A., L vlutzone socle delle occupzon, Il Mulno, Bologn. Duncn, O., A socoeconomc ndex for ll occuptons. In: Ress, A. (Ed.), Occuptons nd Socl Sttus, Free Press, New York. Erckson, R., Goldthorpe, J.H., The Constnt Flux. A Study of Clss Moblty n Industrl Socetes, Clrendon Press, Oxford. Erckson, C.L., Ichno, A., Wge dfferentls n Itly: mrket forces, nsttutons, nd nflton. In: Freemn, R.B., Ktz, L.F. (Eds.), Dfferences nd Chnges n Wge Structures, The Unversty of Chcgo Press nd NBER, pp Glor, O., Tsddon, D., Technologcl Progress, Moblty nd Economc Growth. Amercn Economc Revew, n press. Glor, O., Zer, J., Income dstrbuton nd mcroeconomcs. Revew of Economc Studes 60, Gottshlk, P., Smeedng, T.M., Cross ntonl comprsons of ernngs nd ncome nequlty. Journl of Economc Lterture 35,

43 D. Checch et l. / Journl of Publc Economcs 74 (1999) Geweke, J., Mrshll, R., Zrkn, G., Moblty ndexes n contnuous tme Mrkov chns. Econometrc 54, Glomm, G., Rvkumr, B., Publc vs. prvte nvestment n humn cptl: endogenous growth nd ncome nequlty. Journl of Poltcl Economy 100, ISTAT, Sttstche per vr ordn d scuol, Anno scolstco Rom. Lllrd, D., Nonlnertes n Intergenertonl Moblty n Educton nd Ernngs, Cornell Unversty, Mmeo. Mullgn, C., Prentl Prortes nd Economc Inequlty, The Unversty of Chcgo Press, Chcgo. OECD, Educton t A Glnce, OECD, Prs. Pen, J., Income Dstrbuton, Allen Lne, London. Pketty, T., Socl moblty nd redstrbutve poltcs. Qurterly Journl of Economcs, Schzzerotto, A., Bson, I., Moblt` Occupzonle tr Generzon e Moblt` d Crrer: un Confronto Internzonle (Intergenertonl nd ntrgenertonl occuptonl moblty: n nterntonl comprson. In: Gll, G. (Ed.), L Moblt` Dell Socet` Itln, SIPI, Rom, pp Shvt, Y., Blossfeld, H. (Eds.), Persstent Inequlty: Chngng Eductonl Strtfcton n Thrteen Countres, Westvew Press, Boulder. Shorrocks, A.F., The mesurement of moblty. Econometrc 46, Solon, G., Intergenertonl ncome moblty n the Unted Sttes. Amercn Economc Revew 82, Sommers, P.M., Conlsk, J., Egenvlue mmoblty mesures for Mrkov chns. Journl of Mthemtcl Socology 6, Tremn, D., Gnzeboom, H., Cross-ntonl comprtve sttus ttnment reserch. In: Reserch n Socl Strtfcton nd Moblty, Vol. 9, JAI Press, pp Tremn, D., Yp, K., Eductonl nd occuptonl ttnment n 21 countres. In: Kohn, M. (Ed.), Cross-ntonl Reserch n Socology, Sge, Newbury Prk. US Educton Deprtment, Dgest of Educton Sttstcs, USED, Wshngton. Zmmermn, D., Regresson towrd medocrty n economc stture. Amercn Economc Revew 82,