EDUCATION INEQUALITY AND

Transcription

1 EDUCATION INEQUALITY AND INCOME INEQUALITY Daniele Checchi - Univerity of Milan - Italy Mailing addre: Daniele Checchi Diartimento di Economia Politica e Aziendale Univerità degli Studi di Milano via Conervatorio 7 01 MILANO - Italy tel (dir) 501(ecr) fax daniele.checchi@unimi.it JEL claification: I0; J4; O15; N30 Keyword: Education inequality; Income inequality; Economic growth. Abtract In thi aer we rooe to meaure inequality of educational achievement by contructing a Gini index on educational attainment. We then ue the rooed meaure to analye the relationhi between inequality in income and educational achievement (in term of both the average attainment and it concentration). Even if theoretical conideration ugget a non-linear relationhi between thee two meaure of inequality, actual data indicate that average year of education have a tronger negative imact on meaured income inequality. Multivariate regreion alo rove that, once we take into account the negative correlation between average educational achievement and it dierion, the relationhi between income inequality and average year of chooling i U-haed, with a lower turning oint at 6.5 year. Income inequality i alo negatively related to er caita income and oitively related to caital/outut ratio and government exenditure in education. The author thank the comment of the articiant to the workho on Inequality, growth and overty under the Wahington conenu (Wider - Helinki - July 1999) on an earlier verion of thi aer. He alo thank Meghnad Deai, David Sokice and an anonymou referee for helful comment. Additional thank to the audience of eminar held at Wienchaftzentrum (Berlin), at the London School of Economic, at the SASE conference (London - June 000), Univerity of Pia and Univerity of Piacenza for helful comment. Luca Flabbi rovided excellent reearch aitanthi. Financial uort from the Minitry of Univerity (MURST fondi ex-40%) i gratefully acknowledged.

2 Content: 1. The iue Exiting literature Available meaure of inequality Emirical analyi Concluion Reference Aendix 1 Data ource Aendix Additional table Aendix 3 Alternative education inequality meaure The iue In the literature on the relationhi between income inequality and outut growth, everal author claim that greater income inequality reduce growth. 1 The emirical evidence indicate that one tandard deviation decreae in income inequality raie the annual growth rate of roduct er caita by ercentage oint. However, there i no conenu about the underlying caual mechanim. On one ide, a olitical economy mechanim call for a role for reditributive olicie: greater income inequality generate increaed ocial reure and ocial intability, and thi create an advere environment for invetment in hyical caital. On the other ide, greater income inequality and greater overty inhibit acce to chooling and invetment in human caital, thu reducing the otential for growth. Both exlanation are at odd with a deeer crutiny. The olitical mechanim hinge on the diincentive effect created by fical reditribution, which i not confirmed by the data. The liquidity contraint exlanation require 1 Good urvey of thi literature can be found in Benabou (1996a), Bourguignon (1996), Aghion, Caroli and Gracia-Peñaloa (1999), and Barro (1999). See Perotti (1996). 1

3 that the acce to education be revented by lack of financial reource, which i hardly the cae in countrie where ublic education i nearly cot-free at the comulory level. 3 However both trand of literature make many imlifying aumtion, the main one of which i that income inequality and educational choice are erfectly correlated and that the reulting earning ditribution relicate educational choice. Thi allow the identification of an intergenerational equilibrium in income and education ditribution. Since the two variable are erfectly correlated, the ditribution of income and the ditribution of human caital are haed by the ame factor. In many model, the ame barrier (the abence of financial market for education financing, the cultural overty of the environment, the inefficiency of the ublic adminitration in tax levying) revent invetment in human caital by a fraction of the oulation, who ubequently earn le income. 4 Whenever there i ome intergenerational eritence (via monetary inheritance or the effect of family cultural background), the very ame ortion of the oulation remain traed at low level of education and low level of income for more than one generation. Thu, within the logic of formal model, illiterate eole and the oor are ynonymou. But in reality thing are far more comlicated. Educational choice are alo correlated with the ublic roviion of chool, the rohibition on children labour and the generally available oortunitie in the labour 3 Some emirical evidence in uort of thee rooition i offered in Bourguignon (1994), Checchi (1999) and Filmer and Pritchett (1998). 4 For examle, Galor and Zeira (1993), Banerjee and Newman (1993) and Piketty (1997) conider financial market imerfection, while Benabou (1996a) take into account the role of ocial caital, and Perotti (1993) oint to the tage of develoment and the level of available reource.

4 market. 5 Analogouly, income ditribution can be more cloely related to emloyment comoition, labour legilation, trade union coverage, and fical olicie than to educational achievement among the oulation. 6 However, the ditribution of income and the ditribution of educational attainment are obviouly related. On one hand, income inequality may revent acce to education when education i too cotly for the family: the more kewed the income ditribution, the higher the oulation hare excluded from chooling and the higher the inequality in educational achievement. In thi reect, we have a elf-eretuating overty tra that can only be avoided by eaing acce to education. 7 On the other hand, imroved acce to education raie the earning oortunity of the lowet trata and, other thing being contant, reduce earning inequality. A long a total income i roortional to labour income, we can exect a oitive correlation between the ditribution of educational achievement and the ditribution of income in the oulation. But the other thing being contant aumtion i rather crucial here, ince we have to take into account the general equilibrium conequence of thee change. Conider for examle the cae of kill-biaed technological change. Many author agree that thi i one of the otential reaon for the boot in the college 5 For examle, in rural economie the outut gain of child labour are the main obtacle to chooling among children. See the Zambian cae decribed by Skyt Nielen (1999), the Bangladeh cae analyed by Ravallion and Wodon (1999) and the Indian cae dicued by Weiner (1991). 6 See Gottchalk and Smeeding (1997) and Bardone, Gittleman and Keee (1998) for the determinant of earning ditribution in OECD economie. Globalization and the effect on wage inequality are dicued in Borja and Ramey (1995), Sach and Shatz (1996) and Feentra and Hanon (1996). 7 Checchi (1999) how that income inequality effectively reduce chool enrolment, mainly at econdary level. Similar reult are in Flug, Silimbergo and Wachtenheim (1998). From a formal oint of view, thi correond to the cae where current income inequality affect the rate of change of inequality in educational achievement. 3

5 remium, at leat in the United State. With a time lag, thi ha roduced an increae in college enrolment deite the rie in tuition. Until the uly of new college graduate deree the remium, we will oberve growing income inequality, accomanied by a reduction in inequality in educational achievement. 8 In the reent aer we are concerned with the exiting correlation between the ditribution of educational achievement and the ditribution of income. The literature we have mentioned o far doe not rovide a clear-cut rediction on the ign of thi relationhi. For thi reaon, in thi aer we intend to invetigate the emirical determinant of aggregate income inequality and, more ecifically, the relative contribution of education to meaured income inequality. In our oinion, thi i crucial for two conideration. Firt, from a theoretical oint of view, it i imortant to undertand the lauibility of tudying intergenerational equilibria under tationary ditribution of income and human caital in the oulation. Second, and far more imortant, from a olicy oint of view we want to undertand whether urging countrie (or eole) to increae their educational achievement i going to exacerbate, moderate, or have little influence on the ubequent earning ditribution. The aer i organized a follow. The next ection review the literature on income inequality determinant. The third ection rovide 8 Freeman (1986) ha hown the exitence of a imilar henomenon during the 1960 for engineer in the US and ha rovided a cob-web model for the dynamic of thi henomenon. For more recent evidence, ee Murhy, Riddel and Romer (1998). Galor and Tiddon (1996) reent a model where the oening of acce to education initially widen and then reduce the kill remium. 4

6 emirical evidence. The fourth ection conclude. Aendix I indicate data ource and dicue data reliability. Aendix II rove ome rooition reorted in the text.. Exiting literature There i a growing literature on the current trend in income inequality at world level. 9 Riing income inequality occurred initially in Anglo- Saxon countrie, but now i affecting mot indutrialized nation. 10 Among the otential caue of thi henomenon, the reduction of the reditributive role of the tate, the decline in union reence in the worklace, the increaed cometition at international level, technological rogre and all oible combination of thee are often indicated. However, the exerience at national level are very diverified, and it i quite hazardou to draw general concluion. Aart from the Kuznet (1955) hyothei on the exitence of a non-linear relationhi between outut er caita and income inequality, we do not find much rogre in the tatitical exlanation of the oberved inequality. In articular, little work ha been undertaken o far eeking to tet alternative exlanation of the evidence on income ditribution and even le concerning the relationhi between educational attainment and income inequality. Thi i urriing, given the fact that comulory education i ublicly and freely rovided in almot all countrie of the world. 9 See Atkinon (1999), Cornia (1999) and the reference therein. 10 Milanovic (1999) ha comuted an increae of 3 Gini oint in world income inequality from 1988 and 1993, mainly attributable to between-country inequality. 5

7 At the bet of our knowledge, the exiting literature on the effect of educational attainment on income inequality mainly focue on the two firt moment of education ditribution, namely the average educational attainment (average year of chooling) and the dierion of chooling in the oulation. For the firt, Barro (1999) ugget that the relationhi between income inequality and outut growth i negative for oor countrie and oitive for rich countrie, the threhold being a gro dometic roduct er caita lower than $.070 at 1985 rice. 11 He run conditional convergence regreion on the income inequality (from the Deininger and Squire, 1996, dataet) meaured five year earlier in order to exclude the cae of revere cauation. Then he move thi regreor to the left-hand ide and tudie the determinant of income inequality. He ut forward ome evidence on the exitence of an inverted-u-haed relationhi between outut er caita and income inequality (with a turning oint around $1.636). He control for educational achievement by introducing average educational attainment at three level (rimary, econdary and tertiary). 1 But hi reult are difficult to interret in thi reect, becaue of the contemoraneou reence of different information on the ditribution 11 Perotti roduced ome evidence ointing in the ame direction a dicuant of Benabou (1996b). 1 The anel alo include the average year of chool attainment for eole older than 15, claified over three educational level, rimary, econdary and higher. The reult are that rimary chooling i negatively and ignificantly related to inequality, econdary chool i negatively (but not ignificantly) related to inequality, and higher education i oitively and ignificantly related to inequality (Barro, 1999: 6). 6

8 of educational achievement (namely, the contribution of average human caital and it ditribution acro oulation ubgrou). 13 A imilar trategy i followed by O Neil (1995), who decomoe outut growth over into a quantity comonent (a meaured by enrolment rate) and a rice comonent (a meaured by relative tock of human caital). Hi analyi ugget that, while there i convergence among countrie in the level of educational achievement, the rice effect work in the ooite direction. 14 In the ame line of reearch, Deininger and Squire (1998) how that initial inequality in aet (land) i relevant in redicting both income growth and change in income inequality. 15 Since land inequality alo reduce average year of education in their regreion, they exlain thi evidence by referring to the liquidity contraint on acce to education. A a conequence, income inequality and educational attainment are oitively correlated becaue of the reence of a third conditioning variable (wealth inequality). However, while aet (or income) inequality may reduce the creation of new human caital (the flow rereented by new choolleaver), we ee no good reaon to uoe it might dereciate exiting human caital (the tock rereented by the average educational 13 To be more recie: an additional average year in either rimary chool, or in college hould raie average educational achievement, but the former reduce educational variance in the oulation, while the latter raie it. 14 The reult in table alo how that, for both develoed countrie and Euroe, the rie in the return to education exerienced over the lat two decade ha caued income to diverge ubtantially, a thoe countrie that are better endowed with killed labor rea the benefit of the riing remium (O Neil 1995: 1,95). 15 Low initial inequality i thu doubly beneficial. It i aociated with higher aggregate growth, the benefit of which accrue diroortionately to the oor (Deininger and Squire 1998: 61). 7

9 attainment of the oulation). 16 In a related aer, Li, Squire and Zou (1998) interret the evidence that the effect of (initial-eriod) average econdary chool year on income inequality i ignificant a a roxy for a olitical effect: the more olitical freedom there i, the more informed i ociety, the more difficult it will be for the rich to aroriate extra reource. 17 All thee aer recognize the exitence of a ditributional aect in the relationhi between income inequality and educational inequality, but they rely mainly on average attainment. In contrat, the iue of education ditribution i central in the aer by Loez, Thoma and Wang (1998). 18 They demontrate that human caital, a meaured by average educational attainment, i tatitically non-ignificant in oututgrowth regreion unle one doe not control for the ditribution human caital ( who get what ) or for oenne to international trade ( what to do with education ). They exlain their evidence (on 1 16 In addition, their analyi involve only 5 obervation, and liquidity contraint are rereented mainly not by land ditribution, but by the level of current income. 17 Gradtein and Milanovic (000) rovide additional evidence on the otential exitence of link between olitical incluion and income equality. However, it i not clear which i the direction of cauation: whether extended franchie uort more reditributive olicie, or whether le unequal ocietie trengthen democracy. Jutman and Gradtein (1999) reent imilar idea through a formal model that redict the exitence of an inverted-u-haed relationhi between income inequality and franchie. When the median voter income exceed the average income, regreive reditribution olicie are adoted, and inequality rie; a long a the median voter income remain below the average income, rogreive reditributive olicie tend to be adoted. Finally, Breen and García- Peñaloa (1999) find that greater income inequality i oitively aociated with higher income volatility, a meaured by tandard deviation in outut growth rate, and they how that thi finding i robut even if one control for reviou variable. They ugget that thi could be due to the fact that firm offer an imlicit contract to rik-avere worker. When the environment become more uncertain, the cot of thi imlicit inurance rie, and wage are conequently reduced, thu increaing income inequality. 18 More recently, Amaro and Domenech (001) obtain analogou emirical reult meauring educational inequality by mean of Gini concentration index. Galor and Tiddon (1997) offer another theoretical aer focuing on educational inequality a a ource of technological rogre (and outut growth). 8

10 countrie over ) through reference to the abence of tradability in human caital that make rice equalization imoible and can roduce hortage in human caital during hyical caital accumulation. Along the ame line i the argument by Higgin and Williamon (1999), who redict the Gini index of income inequality uing outut er worker (linear and quadratic, in accordance with the hyothei of Kuznet) and cohort-ize effect (large mature workingage cohort are aociated with lower aggregate inequality becaue of relative exce uly). However, a they exlicitly recognize, thi aroach neglect the endogeneity of educational choice. Let u uoe that a ociety i undergoing a tranitional hae, in which the average educational requirement i riing, uch that the younger cohort are better educated than the older one. Other thing being contant, the maller the ize of the more well educated cohort, the lower the recorded inequality in income. It i therefore rather oible that, through reliance on age-comoition variable, the author were actually caturing educational change. 19 At any rate, the two meaure for educational achievement (average educational attainment and ome meaure of the dierion of attainment) are intertwined. Both Ram (1990) and Londoño (1996) claim the exitence of an inverted-u-haed relationhi between educational achievement and educational inequality, and they locate the turning oint at 6.8 average year of education. 0 However, they do not rovide a ound theoretical argument 19 It i true that they control for econdary enrolment rate, but, a we have already argued above, thi variable meaure the flow and not the ditribution of the tock of human caital. 0 In a ociety where there i no education for everyone, the level of education i zero and the variance of education among the oulation i naturally zero. In a ociety where the entire oulation reache the maximum level of education, the level of education i at maximum, but the variance, again, i zero.... In the interim eriod, the variance of education tend to rie with the increae in the level of education until it reache a turning oint, after which it decreae (Londoño, 1996: 13). 9

11 to exlain thi occurrence, nor do they how whether thi relationhi might hold for alternative meaure of dierion or concentration. 1 What do we learn from thi literature? Three oint eem unquetionable, at leat in the emirical literature: i) income inequality i clearly related to the tage of develoment in accordance with ome ort of Kuznet relationhi; ii) income inequality alo reflect the kill level of the oulation, a roxied by average educational attainment. iii) it i till unclear whether and how average educational attainment and dierion of chooling jointly contribute to hae income ditribution. In addition, in all reviou work, we have not found any meaure related to labour market intitution (uch a the reence of union, unemloyment benefit, or the minimum wage). In the equel, we intend to hed ome light on the third oint by jointly conidering average educational achievement and dierion in the oulation in redicting income inequality. We will alo take into account ome meaure of the quality/quantity of the reource inveted in education. However, thi reaoning i not rigorou on tatitical ground ince a generalized increae of education in the oulation roduce an increae in average achievement without necearily raiing educational inequality. 1 See Aendix II where thi iue i extenively dicued. Nor do we find control for inequality in exlaining emloyment/unemloyment rate. See Glyn and Salverda (000) and Kahn (000) for an analyi of OECD countrie in thi reect. 10

12 3. Available meaure of inequality Starting from enrolment rate and making aroriate aumtion about mortality rate, Barro and Lee (1996) rovide etimate of the human caital tock of a country. Uing mild aumtion on the demograhic (imilar to the ermanent inventory method ued to etimate the tock of hyical caital), tarting from enrolment rate and oeing the ditribution of educational achievement at ome reference time-oint, one can obtain etimate of the average year of education among the oulation for each level of education. Let u illutrate thi with an examle. Conider a oulation in which each age cohort grow at a contant rate n and in which the robability of death i contant acro age and equal to δ. If we define k a the life exectancy, 3 and denote with Po, the oulation aged j at time t, the t j entire oulation i given by Po Po t Pot, k + Pot, k Pot, 0 k t k, 0 1+ i 0 k k 1 k k i i ( 1 δ) + Pot k,0 ( 1 δ) ( 1+ n) Pot k,0 ( 1+ n) Pot k,0 ( 1 δ) ( n) Suoe that chooling conit of one year and droout rate are zero (uch that enrolment rate coincide with graduation rate). Under thi aumtion, if we indicate with π t the ercentage of oulation born in t that achieve education, we obtain the number of eole with education a Po educated t π k t k Pot, k + πt k+ 1Pot, k πt Pot,0 Pot k,0 πt i 1+ i 0 k i i ( 1 δ) ( n) 3 It can be determined a ( 1 ) 0 k : δ. k 11

13 Therefore, under reviou aumtion the current oulation hare with education i given by HC t Pot Po k i 0 π t k+ i k i 0 educated t 1 δ 1+ n 1 δ 1+ n π k i t k k i Po i 0 t, k Po k π + π t, k t k+ i t k+ 1 + Po k ω j 0 Po t, k 1 k i ω k j t, k π Po Po k i 0 π t,0 t k+ i t ω k i t,0 k 1 ω k 1 ω + 1 π t k+ i i 0 k k i i ( 1 δ) ( 1+ n) k i i ( 1 δ) ( 1+ n) i 0, 1 δ ω < 1 1+ n which i a weighed average of at enrolment rate (with declining weight, a in an Almon olynomial). In the articular cae of (1) contant enrolment rate (i.e. π π, i ), equation (1) collae to i HC π. 4 Reeated alication of equation (1) yield 1 ω k 1 ω HC ( ωhc + π ) ( ωhc + π ) Ω, Ω 1 () t t 1 t 1 1 < + t t If we now indicate with HC t the oulation hare with ome rimary education and P t a the enrolment rate for rimary education, both meaured at time t, it i eay to undertand why the former variable can be thought a the integral of the latter (uing the decline rate µ 1 ω a a dicount factor). In ymbol 4 With educational cycle lating more than one year and oitive droout rate, thing are more comlicated, but the logic of the argument hold unchanged. Indicating with λ t the age cohort hare enrolling a chool level lating n year (ay rimary chool tarting at the age of m and lating n year), with a (contant) droout rate of γ, then the enrolment rate would be π t λ t n m+ n k m n n m+ n 1 k m n+ 1 n 1 m ( 1 δ) ( 1 + n) ( 1 γ) + λ t n+ 1( 1 δ) ( 1 + n) ( 1 γ) λ t ( 1 δ) ( 1 + n) m+ n k m n n m+ n 1 k m n+ 1 n 1 m k m ( 1 δ) ( 1 + n) ( 1 γ) + ( 1 δ) ( 1 + n) ( 1 γ) ( 1 δ) ( 1 + n) which in turn i a weighed average of enrolment at firt year, taking into account the decline due to droout. k m 1

14 HC t t t t i {[ HC ( 1 µ ) + P ] ( 1 µ ) + P }( 1 µ ) +... Ω HC ( 1 µ ) + P ( µ ) Ω 1 0 i 1 0 i 1 (3) where HC 0 i the (etimated) oulation hare with rimary education at a given year of reference (uually a cenu year), and µ rereent the (contant) decline rate of an age cohort in the oulation. The ue of a continuou time rereentation yield: HC t t Ω HC 0 ex 0 t ( 1 µ ) + P () ( µ ) d (4) Should the growth rate of the oulation or the mortality rate not remain contant over the year, the above derivation do not correond exactly to the theoretical value imlied by equation (4). By multilying HC by the number of year required to comlete rimary education, we obtain the average number of year of rimary education in the oulation. When we oe thi iece of information for each level of education, we have an aroximation of the ditribution of the human caital tock in a country. The calculation i jut an aroximation becaue in many cae an attained educational level, ay, a econdary degree, may actually be acquired after a longer-than-average eriod of tudy (becaue of reetition); in addition we could encounter eole who attended chool without attaining any certificate becaue earlier droing-out. Even if the information on droout rate i available, we may not know when individual leave a coure of tudy; therefore, we cannot integrate thi information in the comutation of the average 13

15 tock of human caital. 5 Once we have the rough ditribution of educational achievement in the oulation, it i oible for u to calculate everal meaure of inequality, among which the Gini concentration index of the ditribution of attained education i one of the eaiet to comute. If only ubgrou average are known, the general definition of the index i modified accordingly: N N 1 1 G n n n n i j µ i 1 j 1 µ k 1h 1 M M k n h HC k HC h (5) where N i the oulation ize, n i i the number of year of chooling of individual i, µ i the average year of chooling in the oulation, M i the number of ubgrou and n h i the (average) educational attainment in ubgrou h. In the cae of educational attainment, Barro and Lee (1996) rovide u with the available information on three educational level. 6 Thi allow u to divide the oulation in four ubgrou: higher education (a hare econdary education (a hare hare HCh ha attained n h year of education), HC with n year), rimary education (a HC with n year) and a reidual grou without education ( HCn HCh HC HC 1, for which zero education i aumed). 7 By contruction, the average oulation attainment i given by 5 Droout rate are effectively available in Barro and Lee data et at the rimary level. Thi variable range from an average (over the eriod ) of 3.35% in OECD countrie to 39.8% in Sub- Saharan Africa, 39.7% in South Aia and 36.6% in Latin America. 6 Thi i another obviou aroximation, ince we are tandardizing educational ytem into a triartite claification, correonding to UNESCO ISCED (international tandard claification ytem of education level) tandard. However, if a country (like Germany) ha double-track econdary education (high chool and vocational training), each with a different duration, the duration will neverthele be comuted a a though it were a ingle figure. 7 Barro and Lee (1996) make a ditinction between attained and comleted educational level. Given the high correlation between the two erie, we have referred to adot the former variable becaue there are fewer miing obervation for it. 14

16 µ HC HC n + HC n + HC n (6) h h and the Gini index on educational attainment i comuted a follow G ed HC h n h ( HC + HC + HC ) + HC n ( HC + HC + HC ) + HC n ( HC HC + HC ) HC n HC + h n HC ( n n ) + HC HC ( n n ) + HC HC ( n n ) h Starting from the original Barro and Lee (1996) dataet, we have extended the obervation u to We therefore have information about educational achievement in the oulation for 149 countrie at five-year interval over the eriod Overall, thee data cover three-fourth of the 10 countrie lited by the World Bank (1998), but account for 86.3 er cent of the world oulation (in 1990). However, miing value have reduced the otential number of obervation from 1,19 to 848 cae, correonding to 117 countrie (with an average of 7. obervation er country). Decritive tatitic on thee variable aear in table 1 at world aggregate level, in table with temoral diaggregation and in table 3 with temoral and regional diaggregation; additional information about data ource i in Aendix 1. In the mot recent year of obervation (1995), we find that one-third of the world oulation i illiterate; one-third ha rimary education, and the remaining one-third ha econdary chooling or more. During the time an under conideration in thi aer, the average number of year of education roe from 4.3 to 5.8 at the world level, although thi rie wa accomanied by growing ga in the ame variable comuted at regional level. The oulation hare comoed of illiterate eole or eole with rimary education exhibited a declining trend, with ome 15 h h HC HC h n h n (7)

17 reveral at the end of the eriod, and there wa a imilar trend in the index of inequality of educational achievement. But the global icture varied by region: while educational inequality declined in North Africa, South Aia and the formerly lanned economie, it decreaed during the firt three decade, but roe thereafter in other region (eecially in ub- Saharan Africa). Inequality in term of year of chooling remained almot contant at low level in the OECD countrie, deite the increae in the average educational attainment. It i therefore difficult to trace out a ingle trend at world level, eecially becaue there eem to be a difference among countrie in the rate of change, a well a in the level of the variable. Variable Poulation hare without education Poulation hare with rimary education Poulation hare with econdary education Poulation hare with higher education Average duration of rimary education Average duration of econdary education Average duration of higher education Table 1 Decritive tatitic Variable name n 16 Mean (weighto ) Median (weighto ) Std.Dev. (weighto ) Ob. HC 40.4% 43.1% HC 33.8% 3.3% HC 19.8% 17.% HC h 5.6%.5% n n n h n n Average year of education µ Gini index on educational attainment Ginied inequality Gini index on income inequality Gini Table Mean value (weightoulation) acro year Variable Poulation hare without education 46.3% 46.7% 44.1% 44.6% 43.1% 38.6% 33.5% 35.5% Poulation hare with rimary education 38.1% 37.1% 37.4% 34.8% 31.% 3.6% 33.% 3.3% Poulation hare with econdary 1.5% 1.7% 14.0% 16.% 0.4%.5% 5.3%.9% education Poulation hare with higher education.5%.8% 3.5% 4.4% 5.4% 6.3% 8.1% 9.0% Average duration of rimary education Average duration of econdary education Average duration of higher education Average year of education Gini index on educational attainment inequality Gini index on income inequality

18 Table 3 Mean value (weightoulation) acro year regional variation Variable OECD countrie Average year of education Gini index on educational attainment inequality Gini index on income inequality North Africa and the Middle Eat Average year of education Gini index on educational attainment inequality Gini index on income inequality Sub-Saharan Africa Average year of education Gini index on educational attainment inequality Gini index on income inequality South Aia Average year of education Gini index on educational attainment inequality Gini index on income inequality Eat Aia and the Pacific Average year of education Gini index on educational attainment inequality Gini index on income inequality Latin America and the Caribbean Average year of education Gini index on educational attainment inequality Gini index on income inequality formerly Centrally Planned Economie Average year of education Gini index on educational attainment inequality Gini index on income inequality Since we are intereted in the relationhi between educational achievement and income ditribution, we now add the dynamic of income inequality to the icture. Here, we rely on the dataet of Deininger and Squire (1996) and on the World Income Inequality Dataet (WIID) collected by WIDER, both of which contain a ubtantial amount of information on inequality meaure collected from econdary ource. Among thee meaure, the Gini index on income inequality i 17

19 the mot readily available. 8 In the reent cae, we have information on 546 obervation, correonding to 113 countrie (with an average of 4.8 obervation er country). If we retrict our election to the ubet in which there i information about both income and education inequality, we have 478 obervation for 97 countrie (with an average of 4.9 obervation er country; Aendix 1 contain a lit of the countrie). Table reort the oulation-weighted average for thi meaure comuted on all available information in the dataet. 9 We notice that, deite a declining trend in educational inequality (revered only during the 1990), income inequality at world level tarted riing after Figure 1 (which grah the data reorted in Table 3), eem to indicate that thi i mainly attributable to the OECD, the Latin American countrie and the formerly centrally lanned economie. [inert figure 1 about here] One may wonder whether miing value may ditort the amle. Looking at Table 4 we may notice that effectively we oberve an over rereentation of richet countrie and an under rereentation of the ooret countrie, both mainly attributable to income inequality data. If we run robit regreion on data availability (a it i done in Table A1 in the Aendix) we find that under-rereentation involve the lat obervation, the le oulou and the ooret countrie, eecially in the North-African region. On the contrary, Latin American and Aian countrie tend to be overereented. 8 See Aendix 1 for a dicuion of the change made in the original Deininger and Squire dataet, including the 1995 udate of the obervation. 9 Given that the Gini index i not decomoable by oulation ubgrou, the trend in the oulation-weighted average ha to be viewed with caution. See Milanovic (1999) for a more accurate icture baed on oulation urvey (albeit with obervation only over two year, 1988 and 1993). 18

20 World region Table 4 Available obervation for world region otential amle miing income miing education effective amle miing income miing education effective amle OECD countrie % 8.9% 69.8% North Africa and the Middle Eat % 30.6% 17.4% Sub-Saharan Africa % 47.% 16.5% South Aia % 5.4% 55.4% Eat Aia and the Pacific % 3.5% 54.% Latin America and the Caribbean % 0.7% 50.9% formerly Centrally Planned Economie % 8.1% 49.0% Total % 8.9% 40.1% 4. Emirical analyi We now move to the theoretical invetigation of correlation between the ditribution of education and the ditribution of income. So that we can make more recie tatement, let u now conider what we may exect from theoretical model. If we adot a tandard verion of the theory of human caital invetment, initially rooed by Becker (1964) and ubequently taken u by Mincer (1974) to etimate the return to education, the (log)income and year of education are linearly related. In fact, when a Mincer-Becker theory of earning alie, individual earning would be determined a: log( y i ) α + β ni + individual characteritic (gender, age, exerience, etc) εi + (8) where y i i the earning caacity of individual i, ni i the educational attainment of individual i (meaured in year of chooling), β i the (ercentage) rate of return to education and α i the earning of an individual without formal education; ε i i an error term aumed to be i.i.d. (identically indeendently ditributed). If we aume that the individual characteritic are idioyncratic in the oulation and orthogonal with acquired education, oulation ubgrou differ only 19

21 in term of average educational achievement (namely, the within-grou variance i contant).if we aume that the individual characteritic are idioyncratic in the oulation and orthogonal with acquired education, oulation ubgrou differ only with average educational achievement (namely the variance within grou i contant) 30. We therefore exect there to be a relationhi between the ditribution of educational achievement and the ditribution of actual income. However, the thing are not o imle. Inerting equation (8) into equation (7) and ignoring the (average) individual characteritic, we obtain the Gini index of log-income inequality a: G log income HC h β n h ( HC + HC + HC ) + HC β n ( HC + HC + HC ) + HC β n α + β HC n h α + β HC ( HC HC + HC ) n h n + (9) or more ynthetically G HC G α + HC β ( HC) f HC log income ed (10) ± Equation (10) ugget that, at a given average in educational achievement, the inequality in education and the inequality in (log)earning are linearly related. If income are roortional to earning, thi alo alie to inequality in (log)income. However, ince the inequality in education i negatively related to average education, the actual relationhi i non-linear. 31 The ituation i rendered more 30 Actually, Mincer (1996) how that between-grou variance in earning ditribution in the US remained nearly contant during , wherea the within-grou variance exanded after the In a reviou verion of thi aer, we made ue of imulation (relying on the oberved value for educational achievement) to analye the relationhi between education and income inequality under 0

22 comlicated by the fact that we do not oe individual data allowing the calculation of inequality meaure for (log)income. Rather, we are forced to rely on aggregate meaure baed on actual income. Once more, the relationhi between the inequality meaure obtained from actual value of the variable and the correonding meaure comuted baed on the logarithm i not eaily acertained (unle we imoe more tructure to the roblem by auming a ecific functional form for the frequency ditribution). However, it can be formally demontrated that under mild aumtion about the ditribution of education in the oulation and the general aumtion that the rate of return to education i contant the relationhi between the Gini index of actual income and the average year of education initially rie and then decline. 3 When the aumtion hold, income inequality, education inequality and average educational inequality are trictly related, a hown in Figure, where we have alo added a fourth variable, the outut er caita, in order to control for an exogenou driving force. Starting from the lower right-hand quadrant, we aume that an increae in er caita income i aociated with an increae in the average educational attainment. By contruction, thi yield a the aumtion that return to education are contant. We found that the relationhi i oitive and tronger in countrie with low-to-middle inequality in education (lower than 45%), wherea the ame relationhi i negative in countrie with very high inequality in education. Thi i becaue the Gini concentration index i cale invariant (that i, it doe not vary when we change the unit of meaure), but not tranlation invariant. Therefore, given the reence of a contant (α 0), a generalized rie in educational achievement (at the given inequality in educational attainment) induce a change in income inequality. 3 See the Aendix 3. 1

23 conequent decline in educational inequality (lower left quadrant). 33 If the relationhi between average educational attainment and income inequality i non-linear, thi necearily imlie a non-linear relationhi between income inequality and education inequality (uer left quadrant). By the ame token, we alo obtain an inverted-u-haed relationhi between income inequality and er caita income, in the Kuznet tradition (uer right quadrant). The grah tell u a tory about the tranition from an uneducated oulation to an actual level of chooling. When only the élite attend chool, the average level of human caital develoment among the oulation i low, wherea the inequality in educational achievement and in income i high. A lowering of the acce barrier to education lead to an initial increae and then to a decline in both inequality meaure, and thi i accomanied by a rie in average educational attainment. A imilar tory i obtained in the model reented by Galor and Tiddon (1996). [inert figure about here] A firt inection of our dataet indicate that thi tory may have ome lauibility. Figure 3 gather together all the available obervation, whereby income inequality i meaured by regreion reidual on regional dummie and year-related dummie in order to comenate for trend in the variable and regional diaritie. In addition to a mildly non-linear relationhi between inequality in actual income and inequality in education (ee the uer left quadrant), a imilar relationhi emerge between the former variable and (the log of) GDP er caita, in line with the Kuznet tradition (uer right quadrant). Without concerning ourelve too much about the direction of the caual 33 See, again, the Aendix 3.

24 relationhi, we alo find evidence of a trict oitive correlation between outut er caita and educational achievement (lower right quadrant). Finally, by contruction, we find an inverely roortional relationhi between inequality in education and average educational achievement (lower left quadrant). 34 However, the dierion of ingle obervation ugget that many other force are at work. We hould not forget that the validity of the tory of Figure i conditional on the aumtion that individual income are determined according to Becker theory of human caital invetment and that return to education are contant and are, moreover, identical throughout the oulation and acro countrie. In reality, we know that earning ditribution i haed by many other factor, including technology, unemloyment rate, minimum wage, age comoition, the exitence of labour union, and o on. 35 Were it certain that thee factor remained contant during our amle eriod, we could conider them country-ecific fixed effect. The roblem i that there i no guarantee that they remained contant, eecially if we 34 However, the way we meaure educational inequality i crucial. Had we choen the tandard deviation of educational achievement like Ram (1990), Londoño (1996) and IDB (1998), the relationhi between average educational attainment and educational inequality would have aeared non-linear: St. Dev. ed HC HC, R 0.3, n 848 (4.4) (19.6) (17.8) In uch a cae, the turning oint would occur at 5.75 year (rather than the 6.8 year meaured by Ram, 1990). 35 See Neal and Roen (1998) for a general reentation of determinant of earning ditribution. Higgin and Williamon (1999) find evidence of an effect of age comoition (a meaured by the hare of individual aged in the labour force) in determining income inequality. With reference to OECD countrie, Bardone, Gittleman and Keee (1998) how that labour market intitution changed during the amle eriod: trade union denity and coverage declined (eecially within the Anglo-Saxon world), while minimum wage declined almot everywhere, and cut to welfare aitance may have induced lower reervation wage. 3

25 take into account the tranformation in ublic olicie induced by the tranatlantic conenu (Atkinon, 1999). [inert figure 3 about here] A a conequence, intead of retending to redict the hae and the evolution of income ditribution worldwide, we follow in the equel the le ambitiou aim of dicovering whether the average educational achievement and the ditribution of educational attainment have layed any role in determining income inequality. We have already mentioned the fact that other author (Londoño, 1996; Deininger and Squire; 1998; Barro, 1999) have hown that average educational achievement i one of the determinant of actual income inequality. To thi reult, we now add an examination of the effect on income inequality of the ditribution of educational achievement in the oulation. In order to take into account the imultaneou effect of all the variable, we reort to multivariate regreion. We take our dataet a an unbalanced anel with a otential dimenion of 75 obervation (94 countrie time 8 obervation er country), which we reduce to 454 obervation becaue of miing data on one or the other variable. Table 5 how etimate of actual income inequality uing fixed effect, wherea Table A in Aendix relie on random effect etimator. In both table we tart with two alternative ecification of the relationhi between income inequality and outut er caita, without taking into account educational factor (firt and econd column). Both ecification reject the hyothei of a non-linear relationhi between income inequality and er caita outut. The two meaure are negatively correlated, with a rather low elaticity ( at amle 4

26 mean). Thi imlie that, in order for the Gini index of income inequality to be reduced by 1 oint, income er caita ha to rie by $,311 (at 1985 international rice). If we relace er caita income by educational variable (third and fourth column), we notice an increae in exlanatory ower only if we conider average educational achievement. Thi i not urriing given the high correlation of the latter meaure with er caita income. Both average educational achievement and educational inequality are ignificant, but the relationhi between the two meaure of inequality i ooed to the theoretical exectation (being U haed and not inverted-u haed). We conider GDP er caita and educational variable together in the fifth column. Here, we find that outut er caita ha a low negative imact, a doe average human caital, though with a higher effect: an average increae of one year of education in the oulation lower the Gini index of income inequality by more than 1 oint. The ixth column offer an alternative (hyerbolic) ecification of the functional relationhi relating income inequality and average human caital: given the non-linear relationhi exiting between the Gini index of educational inequality, the variable 1 / h eem able to cature all the c exlanatory ower contained in the educational ditribution variable. 36 However, the exlanatory contribution of the ditribution of educational achievement i region ecific and rather untable. If we run fixed effect etimate for world region (a in Table 6), we ee that education 36 However, thi reult i not robut. When we introduce a roxy for technological rogre (the caital/outut ratio) in the regreion (ee Table A in Aendix ), the inequality in educational attainment retain it ign and ignificance even with the hyerbolic functional form. Notice that the number of obervation i reduced under thi ecification becaue we do not have information about national caital tock for 18 of the countrie. 5

27 ditribution variable are ignificant for OECD countrie, Latin American and Sub-Saharan countrie, that i the countrie at the extreme of income and/or education inequality. 37 When we include reeated cro-ectional etimate (a in Table 7), we find that the average educational achievement and the Gini index of educational inequality (in level and quared level) are tatitically ignificant in five of eight cae, but now the non-linear relationhi i of the inverted-uhaed tye (which i in line with human caital invetment theory). One otential reaon for thi intability i that omitted variable might contribute to a reverion in the trend in income inequality. In Figure 4 we have grahed the coefficient of yearly dummie obtained in the regreion reorted in the fifth column of Table 5 and A. Thee coefficient (normalized by the coefficient of the initial year) meaure a hift in the intercet of the regreion, thu caturing art of the variance that i left unexlained by the etimated model and that i year ecific. For the firt half of the amle (until 1975), we witne a growing reure for the comreion of income ditribution (on the order of 1 oint in the Gini index every five year), wherea thi effect diaear during the In the 1990 the henomenon work in the ooite direction, favouring widening income diarity. [inert figure 4 about here] Since by definition yearly/regional dummie cature unexlained comonent, we do not have reliable exlanation for thee effect that 37 Regional dummie (ued in the etimate of random effect reorted in Table A) indicate that the greatet inequality wa regitered in Latin America and ub-saharan Africa, where inequality indexe were 6 ercentage oint higher than they were in the OECD countrie (which rereent the reference cae; ee the fifth column in Table A). Converely, the ditribution wa more egalitarian in the currently (or reviouly) centrally lanned economie, where the Gini index wa 1 ercentage oint lower than it wa in the OECD, and in South Aia, North Africa and the Middle Eat. 6

28 do not refer to er caita income or educational achievement. Neverthele, we have exerimented with two additional variable that may cature ome of the difference among countrie or year. The firt one i the hyical caital/outut ratio. On theoretical ground, if hyical and human caital are ubtitute in the aggregate roduction function, an increae in the former raie the roductivity of the latter. Therefore, cœteri aribu, we will obtain higher return to education whenever hyical caital accumulation become more intenive. Thu, we can exect greater income inequality whenever and wherever there i intenive invetment in hyical caital. 38 Thi variable i introduced in Table 7 and alo in Table A3 in Aendix (which reroduce information in Table 5, though the number of obervation i reduced becaue of miing information). Thi variable i not very ignificant in the fixed effect etimate, but ha a oitive and ignificant ign in the reeated cro-ectional etimate (u to 1985). Other thing being contant, countrie characterized by higher accumulation in hyical caital alo exhibit higher income inequality: aing from an average k / y ratio of in South Aia to 3 in the OECD countrie raie the Gini index of income inequality by (u to 5) oint. However it i inignificant in more recent year. The econd variable we take into account i the amount of ublic reource inveted in education. If the technology for human caital formation include inveted reource, we can exect increaed human caital er unit of time ent in chool whenever education exenditure 38 Thi claim i objectionable when we think of information and telecommunication technologie, for which the caital/outut ratio i actually lower than it i for manufacturing, notwithtanding the fact that the earning differential are higher. 7