Gone for Good? Determinants of School Dropout in Southern Italy

Transcription

1 DISCUSSION PAPER SERIES IZA DP No. 39 Gone for Good? Determinant of School Dropout in Southern Italy Niall O'Higgin Marcello D Amato Floro Erneto Caroleo Adriana Barone January 008 Forchungintitut zur Zukunft der Arbeit Intitute for the Study of Labor

2 Gone for Good? Determinant of School Dropout in Southern Italy Niall O Higgin Univerità di Salerno, Celpe and IZA Marcello D Amato Univerità di Salerno and Celpe Floro Erneto Caroleo Univerità di Napoli Parthenope and IZA Adriana Barone Univerità di Salerno and Celpe Dicuion Paper No. 39 January 008 IZA P.O. Box Bonn Germany Phone: Fax: iza@iza.org Any opinion expreed here are thoe of the author() and not thoe of IZA. Reearch publihed in thi erie may include view on policy, but the intitute itelf take no intitutional policy poition. The Intitute for the Study of Labor (IZA) in Bonn i a local and virtual international reearch center and a place of communication between cience, politic and buine. IZA i an independent nonprofit organization upported by Deutche Pot World Net. The center i aociated with the Univerity of Bonn and offer a timulating reearch environment through it international network, workhop and conference, data ervice, project upport, reearch viit and doctoral program. IZA engage in (i) original and internationally competitive reearch in all field of labor economic, (ii) development of policy concept, and (iii) diemination of reearch reult and concept to the intereted public. IZA Dicuion Paper often repreent preliminary work and are circulated to encourage dicuion. Citation of uch a paper hould account for it proviional character. A revied verion may be available directly from the author.

3 IZA Dicuion Paper No. 39 January 008 ABSTRACT Gone for Good? Determinant of School Dropout in Southern Italy * The aim of the preent paper i to gain ome inight into the caue of dropping out of chool and, more generally, of the factor that induce parent to review their choice about their child chooling career. To thi end we apply to data from a chool dropout urvey inight from a model of equential deciion making by parent, where the initial deciion can be reviewed in the light of new information emerging about the ability and opportunitie of the child in benefitting from education relative to her outide (in the unkilled market). Analyi of the data confirm the role of both economic capacity (opportunity cot) and cultural capacity (ability to dientangle ignal about future opportunitie) of the family of origin hape oberved choice about drop-out and return to chool by individual in our ample. Dropping out behaviour alo appear to be trongly influenced by mimatche between chool and tudent, however, and many of thoe who leave are not gone for good. JEL Claification: I, J3, J4 Keyword: young people, chool dropout, human capital Correponding author: Floro Erneto Caroleo Department of Economic Univerity of Naple Parthenope Via Medina Naple Italy caroleo@uniparthenope.it * We acknowledge financial upport from the Province of Salerno in undertaking the urvey on which thi paper i baed. Thank are alo due to participant in the workhop on Education Supply and Demand in Italy, Turin, 8 May 007 and at the AIEL conference in Naple, 3-4 September 007 and in particular to Daniele Checchi and Giueppe Bertola, who alo organied the Turin meeting, along with an anonymou referee for their inightful comment on previou verion and which we very much hope lead to the paper ubtantial improvement. Unfortunately none of thee can be blamed for any remaining error of omiion or commiion which remain firmly with the author.

4 . Introduction In thi paper, data from the chool dropout urvey undertaken in Salerno Province by the Centre for Labour Economic and Economic Policy (CELPE) are analyed. A key feature of our ample i that a ubtantial proportion of chool dropout ubequently return to ome form of education. Abandoning chool for a period and then poibly returning to education in a different chool i obviouly an indication of ditre and ugget that education choice are ubject to everal kind of error and mitake: mitake parent make about the kid ability to purue a pecific education career, change in the child attitude toward chool in a period of their life (adolecence) when her character, ocial kill and pecific capacity to adapt to learning and education evolve and are ubject to hock omewhat not perfectly controlled or forecated by familie. Thee ocial and pychological apect make the tudy of thee problem from the economic point of view quite entangled. From a purely choice theoretic perpective, parental apiration and their choice about their child educational career involve ubtle pychological and ociological apect not eaily quared with a imple invetment approach to education choice. Such choice may be reviewed in the light of the new information about opportunitie and abilitie that unravel when the child grow a an adolecent. Thi new information may arie from parental experience about the cultural evolution of the young man a a tudent, about the quality of the match between a pecific child and a pecific chool or teacher, or imply about the opportunity cot of education given what parent ee a the return to have their child educated. However, even if it i a hard tak to quare deciion made by adolecent and their parent during thi period of the child life with a choice theoretical framework, tudying the economic implication of thee deciion i important from an economic perpective. Choice made during childhood have important effect later in life, haping the detiny of the young peron both in term of ocial tatu and of economic return of invetment in human capital made during adolecence. More generally, the preence of mitake and error may be an indication of an inefficient allocation of talent to chool track during adolecence and therefore, given the large involvement of public reource in the education ytem, the tudy of thee problem i very important alo from the perpective of policy deign a well.

5 The aim of our work i to gain ome undertanding of the caue of dropping out of chool and, more generally, of the reaon that induce parent to review their choice about their child chooling career. The paper propoe a model of equential deciion making by parent where the deciion can be reviewed in the light of new information emerging about the ability and opportunitie of the child in profiting from education relative to her outide (in the unkilled market). The model allow interpretation of uch dropout and return behaviour and emphaie the eparate role of both economic and cultural capacity (a regard the ability to dientangle ignal about future opportunitie) for equilibrium deciion making. On the other hand, being a partial equilibrium model, we do not tackle efficiency iue that obviouly arie, and ue the model a a guide for the implementation of the analyi of the data and a a theoretical framework to interpret empirical reult. Specifically, the nature of the theoretical model lead fairly naturally to the implementation of a cenored bivariate probit model of initial dropout and return to chool by young people. The ret of the paper i organized a follow: in ection we preent ome tylized fact and ome related literature, in ection 3 we preent the model, in ection 4 we preent the empirical reult; ection 5 conclude.. Some Stylied fact and a glance at the literature The Libon agenda include everal quantitative target for education and training ytem in Europe. One pecific goal i reducing the hare of early chool leaver i.e. 8-4 year-old with at mot a lower econdary education qualification and not in further education to le than 0% by 00. (Commiion of the European Communitie, 00). The reaon i that riing kill demand imply the neceity of the completion of at leat upper econdary education for ucceful labour market entry and for further participation in lifelong learning (ee OECD, 000). Even though preent trend how, in general, clearly decreaing level of early chool-leaver in the Member State - epecially in Spain, Italy, Greece, France, Belgium and Finland - (Quintini and Martin, 006), further effort are required to enable the EU to reach the target, a the lo of tock of human capital i till unacceptably high. A recent analyi carried out by the Minitry of Public Education (Minitero della Pubblica Itruzione, 006, pp. -3, tab.7) point out ome peculiaritie of the drop out phenomenon in Italy, underlining that: 3

6 - both failure at chool and dropout are o widepread that about a third young men and more than one-in-five young women enrolled in upper econdary chool do not obtain the diploma ; - female educational performance i better than male, particularly in technical and vocational chool; - tudent attending claical and cientific chool have the highet probability of completing their tudie in all the geographical area of Italy while thoe attending technical chool in the North of Italy have a lower probability of completing their tudie than in other area. Thi may plauibly be explained by the, at time oppoing, motivation for dropping out related to the opportunity cot of, and expected (employment and income) return to education. Thu, dropping out i a characteritic of both depreed and developed area. The early entry into the labour market in Lombardia and other area in the North-Eat where the labour demand i high can caue a crowding effect of the chooling and training ytem, raiing the rik of lower qualified occupation in the future (table ). Table : Probability of obtaining final diploma by gender, geographical area and type of chool (graduate from the chool per 00 enrolled at the firt year 5 year before) Upper econdary chool public and private - year Total Scientific and claical Pychopedagogical Technical Vocational Art TOTAL 7,3 85,6 8,3 79,0 47,8 6,9 North 7, 85,3 84,7 73,4 5,3 68,5 Centre 74,4 86,7 78,5 8,3 48,4 6, South and Iland 7,4 85,4 8, 8,6 44,8 59,5 MALES 67, 84,7 87,5 74,5 4,5 56,7 North 64,7 83,5 90,7 67,9 43,8 59,5 Centre 69,7 88,7 69,9 75,9 4, 55,8 South and 67,9 83,8 9,5 79,6 39,7 55, Iland FEMALES 78, 86,3 8,5 87,6 56,5 66,0 North 78, 86,8 83,8 83, 60,3 7,6 Centre 79,5 85,3 80, 95,5 56,5 63,8 South and Iland 77,5 86,5 80,6 88,6 5,9 6,8 Source: Minitero della Pubblica Itruzione (006b, table 7, p. 3) 4

7 Concerning the cae under tudy, table report reident at the beginning of the year by age in the Province of Salerno and tudent enrolled in the chooling year Each age group comprie individual. The gap between the number of thoe enrolled and age-pecific age population i around 0% of the population which in itelf provide a very rough indicator of the extent of dropping out before completion of econdary chool. Moreover, both the number enrolled and the proportion in State chool decline from 5 to 8 year. The firt phenomenon i an apect of what i known chool diperion and the econd ignal that tudent hift from public to private chool in order to become econdary chool graduate. Age Table : Number of the reident and enrolled in the Province of Salerno by age Total reident at 0/0/03 Men Total reident at 0/0/04 Men Total reident at 0/0/05 Men Enrolled to chool (A) Enrolled to public chool (B) Enrolled to public chool/ enrolled to chool (A/B) (%) Total Source: Itat ( ) and Minitry of Public Education (006a) Data taken from the 00 Cenu of Population and reported in Table 3 confirm that the number of reident aged 5-8 in the Province of Salerno not enrolled to a regular coure of tudy increae a the age increae. In the lat decade the Italian authoritie, aiming at reducing drop out rate, have opted to change the minimum chool-leaving age introducing compulory chooling and training up to age 8 (Law n.44/999 obbligo formativo and Law n.53/003 diritto dovere all itruzione e alla formazione ). The intitutional actor, public or private, involved in the realization of uch obligation are manifold (School, Training Centre, Employment Agencie) and at different level of governance: central (Minitry of Education) and local (Region, Province, Local Employment Agencie). The duty of all of them i to follow the tudent in puruing their tudie and to make eaier the chool-to-work tranition, developing broad-baed community partnerhip aimed at helping at-rik youth. 5

8 Table 3. Number of the reident and enrolled/not enrolled in the Province of Salerno Age Reident (A) Enrolled in a regular coure of tudy (B) Not enrolled in a regular coure of tudy (C) (C/A)% Totale Source : ISTAT(00) Student who drop out face a lot of economic and ocial difficultie. Several tudie find that adult earning are higher when tudent are compelled to take an extra year of chool (Oreopoulo 007; Angrit and Krueger 99; Acemoglu and Angrit 00; Blundell, Sianei and Dearden, 003). The poitive ocial externalitie are alo coniderable. Drop out are more likely to be unemployed, reporting poor health, being depreed, being in a low killed manual occupation, drawing on ocial aitance and other welfare program, and to end up in jail (Lochner and Moretti 004). Many factor have been identified a influencing dropping out. Some are chool-related: a drop out doe not like chool in general or the chool he/he i attending, he i failing, getting poor grade, or cannot keep up with chool work, he doe not get along with teacher and/or tudent. Other factor are tudent-related: a drop out ha diciplinary problem, i upended, or expelled, he doe not feel afe in chool, he ha different trait than thoe who graduate (Ecktein and Wolpin, 999) for example: low ability and/or motivation, low expected return to graduation, better market opportunitie for the job that don t require graduation, lower conumption value of chool attendance. Reaon for dropping out may be related to peronal problem a well: drug and alcohol abue, obeity or health problem (Celpe 006). Other factor are family-related: treful/untable home life, lack of family upport, ocioeconomic tatu, ingle-parent houehold, poor education of parent, deire to get married and/or getting pregnant (Cardoo and Verner, 006). There are alo ome categorie of youth that are at more at rik of dropping out: certain ethnic group, tudent living in large citie or in a poor area, or attending chool whoe tructure or academic and ocial organization may not favour the holding in of tudent at rik (Lee and Burkam 003). 6

9 The tandard human capital model aume that tudent are rational and time conitent, o the choice of the optimal education attainment level may be treated a an invetment deciion (Becker 964; Card 999). That level i defined by the point where the opportunity cot from additional chooling outweigh the benefit. Student who decide to drop out becaue of pychological or motivational problem, are imply evaluating that forgone earning and effort cot from attending chool are higher than the etimated expected benefit. However, it i widely recognized that the tandard model cannot completely explain drop out behaviour. Policymaker want to update compulory chool law and to introduce retriction on the choice of tudent becaue they are peruaded that leaving econdary chool before graduation i a uboptimal outcome. Oreopoulo (007) find ignificant lifetime reward to wealth, health, and overall happine from having to take another year of chool a well a ubtantial income gain o that diutility from not attending chool i very high. There are other reaon that may account to ome extent for the deciion to leave the chool. Credit contraint may mean that tudent, epecially thoe from low income familie, cannot borrow againt the expected higher outcome to finance the ex ante optimal level education (Carneiro and Heckman 00). Myopic behaviour of drop out may alo lead to a imilar outcome. Student may give greater emphai on the preent, becaue they make erroneou prediction of future return or underetimate the real gain from chool or have negative expectation about the future, o they attach more weight to the current non pecuniary or monetary cot in calculating the chool attainment deciion. Sociological and pychological reearch point to the importance of a tudent ocial group in determining their active involvement in chool. Thi literature (for a review ee Akerlof and Kranton 00) conider chool a intitution, with ocial goal beide imparting kill, and highlight that educational outcome of tudent depend on their identification with the chool' ocial category and it ideal tudent. A further apect that ha been invetigated i the role that chool their tructure, their academic organiation and their ocial organiation- play in tudent deciion to tay in chool or leave before graduating (Lee and Burkam 003). Factor related to chool quality are alo important in determining whether tudent who leave their high chool either tranfer to another chool (and thu tay in chool) or leave chool altogether (Rumberger and Thoma 000; Hanuhek, Lavy and Hitomi 006). Different dropping out explanation, obviouly, call for different policy deign. Compulory chool legilation may be effective when taying in chool ha ignificant benefit in term of future reward to wealth and well being. On the contrary, policie aimed at forcing tudent to remain in chool until they 7

10 graduate may have little impact if the reaon for leaving chool are related to the individual characteritic: the lack of motivation, low ability, or the greater preference for low killed job. In thi cae, it become neceary to alter the trait with which youth come to high chool. Policy option, aimed at reducing the cot of chooling (both direct and indirect) or offetting immediate cot with immediate benefit, may improve the tudent kill upgrading when drop out do not correctly evaluate the future return to chooling becaue of a myopic behaviour or becaue of the family background, credit contraint, extremely poor economic and ocial environment. A noted above, pychologit and ethnographer often point at the importance of a tudent attitude toward chool, rooted in their ocial and cultural background, in influencing their chool choice deciion, o it become important that chool reinforce the ocial incluion and the ocial identity of their tudent. Finally, ociological theory tree alo the relevance of organizational and tructural characteritic of chool -i.e. ize and ector, curricula offered, the character of relationhip between tudent and teacher, etc.- in the deciion of tudent, implying that policymaker have to pay a pecial attention to trengthen the quality of chool. 8

11 3. A framework for the analyi. A imple model of parental equential choice about their children chooling career. In thi ection we build up a framework for the analyi of the main determinant of the deciion to quit chool, and poibly return to it, after having pent a period out. The model i baed on a imple idea of repeated learning by parent about their children abilitie and (future) job market opportunitie. Sending the child to chool allow parent to ae their ability in the labour market and formulate expectation about the child wage on the killed labour market relative to the unkilled one. The main building block of the model are a follow: parent ue chool ignal to extract information about their child ability a a killed worker baed on their prior belief and on the evidence provided by chool aement. If the ignal at chool i bad, parent re-ae the value of invetment in human capital depending on their private ignal on the child ability. After balancing the private with the public ignal (the relative preciion of thee being crucial for the aement) parent make a deciion about chool enrolment in ubequent grade. If the child leave chool, he pend a period out of education and further information accrue to her parent about her pecific ability in the unkilled job market. Conditional on thi information, parent may decide to leave the child outide chool or to give her a econd chance to proceed in education. Thi latter hypothei, i.e. that ome information about future alternative opportunitie to the child i collected when he pend a period out of chool, i the key element to undertanding the proce of re-entry. Parental capacity to ae their child quality and ue the public ignal at chool, along with the opportunity cot of education and ome form of irreveribility of education choice will determine the equilibrium choice in thi model: parental culture (preciion of the private ignal of the child ability), chool quality (the preciion of the public ignal provided in grading the child performance at chool), and economic tatu (the opportunity cot of educational invetment) matter in our framework. A for irreveribility we will aume that high chool can only be completed when the child i adolecent and tay with her parent. We will alo aume that after completing high chool the deciion about the young peron future career (univerity veru unkilled labour market) i irreverible. The identification of the parent() a the deciion-maker rather than the individual directly concerned align thi paper with the convention uually adopted in overlapping generation model, rather than the tandard human capital model which tend to identify the (potential) tudent a the deciion-maker. Indeed thi may look trange to reader more familiar with the latter type of model. However, the crucial implifying aumption here i that there i a ingle deciion-maker rather than who that deciion-maker i. For a model with altruitic parent chooing their children human capital invetment ee, for example, Mookherjee & Ray (003). 9

12 Specifically, we conider two baic path leading the child to being prepared, a an adult, either for the killed labour force (ay univerity enrolment) or for the unkilled labour force. We aume that deciion are made by altruitic parent. Thee choice are baed on the parental aement of the benefit of the child chooling alternative, given their expectation about wage in the killed and unkilled labour market. Thee aement regard the child ability in the two labour market. School i aumed not to add kill valuable on the job market, thi i a trong implification but a richer role for chool could eaily be conidered within the model 3. Choice are made equentially, conditional on the ignal parent get about their children ability and their market opportunitie. In making their equential choice, parent trade-off thee benefit with their opportunity cot of having their children educated. Sequentiality of choice reviewed in the light of the new information i modelled a follow. We divide the child time horizon (call it adolecence) for the family deciion into three period. The exitence of compulory baic education mean that parent have to end children to chool for at leat one period at the end of which a ignal i collected about the child ability. At the beginning of period two, parent make a choice about the child future career: either they withdraw him from chool or they have him complete hi education. Thi choice i made conditional on the ignal being collected at chool in the firt period (educational core at chool in period one) balancing it with their prior about the child ability. If parent chooe to leave the child at chool he complete hi chooling career in period two and ha to decide whether to enrol at a higher level (univerity, ay) or get back to the unkilled labour market. Conditional on the parental deciion to withdraw the child from chool at the beginning of the econd period, we aume the child pend a period out learning hi alternative opportunitie on the unkilled labour market 4. Again, after having pent a period out of chool and having obtained a ignal about her 3 For a richer view of child identity and education ee Akerlof and Kranton (00). Auming education i productive would increae the incentive to tay in chool and, where relevant, to return after dropping out but would not change the implication of the model. 4 The decription of a period out of chool during adolecence ha to be interpreted in quite broad term. It may vary depending on the actual ocio-economic context in which the family invetment in educating their children i cat. For example in le developed countrie or area, where agriculture or mall cale family buine play important role, failing at chool will likely involve for the kid a period of actual training in the traditional occupation. In more developed countrie or region kid failing at chool may only involve further information acquiition by parent about alternative opportunitie (thi information acquiition by parent may range from a more careful invetment in the parent-child relationhip entruting a pychologit or a private tutor, dicuing the iue with friend and relative to better ae the child talent for alternative occupation. We do not enter into uch detail- which can be quite important- ince our working hypothei i meant to deal with everal pecific ocioeconomic environment: after the kid i perceived to have failed at chool parent have incentive to review their prior about the kid talent in different occupation and condition their education invetment upon thi new information. 0

13 child opportunitie on the (unkilled) labour market they make their deciion again: they can leave the child in the unkilled labour market or have her return to chool. At equilibrium, in each family, choice about a child career will depend on the kill premium expected given the ignal (i.e. the relative expected benefit from the two alternative path), the opportunity cot of education, and on the preciion of the ignal about the child potential ability a a killed worker (at chool) and her opportunitie on the unkilled job market. To analyze the model we make a bunch of implifying aumption none of which will affect our main reult whoe economic will turn out to be quite intuitive. We aume that there i one parent and one child, the deciion i made by the parent, leaving the child with no meaningful deciion. Our model i a partial equilibrium model, i.e. we do not derive the equilibrium level of the kill premium a a function of family choice. Learning occur optimally given the information accruing to parent a time unravel. We will aume rik neutrality in parental utility and that all the ignal ued for parental deciion and the parameter on which the deciion making i made contingent on are normally ditributed 5. We alo aume no dicounting by parent and, jut for implicity, no tuition fee for high chool enrolment with anticipated cot of univerity enrolment being equal to T 6. A already dicued, once children complete high chool, the choice between going to univerity and working in the unkilled labour market become irreverible. Analogouly, after two period in the unkilled labour market children are not allowed to return to chool. Thi i equivalent to making the cot of witching back to education after a certain age ufficiently large. A le dratic aumption would have been to provide parent and children with the option to witch acro educational career for a longer horizon at a moothly increaing cot. Thi aumption i only made to avoid recurive formulation of the more general dynamic programming problem that would arie in the abence of complete irreveribility. Thi richer formulation would not change the main reult, however. Finally we aume that the children abilitie are relevant on the killed labour market but are not on the unkilled labour market 7. Thi will implify the derivation of the formula for the information updating proce by the parent quite a bit, but again, mot of the reult would go unchanged with a more general role of ability in both market. More pecific comment about thee aumption will be provided in the following. 5 Both thee aumption can be dipened with the reult going almot unchanged if we aume rik averion on the child benefit and rik neutrality with repect the parent income and i.i.d propertie of the hock accruing to parent information et. 6 Which may include perceived conumption cot a well a tuition fee and the like. 7 Equivalently the aumption i that child ability index valuable in the killed labour market i independent of the ability index that define the child market opportunitie in the unkilled labour market.

14 The detail of the deciion making proce and the time line faced by parent are a follow. At time t=0 parent enrol their child at chool. The child ability i denoted α, which i equal to the child value (productivity) expected on the killed labour market (denotedα parental belief by the relation: w ), and i related to () α = θ + ε, where θ i the parent initial aement, ε i the noie affecting parental judgement. We aume the ignal θ i unbiaed 8 i.e.,ε follow a normal ditribution with mean 0 and variance. Thi latter can be family pecific and reflect cultural heterogeneity among familie in their capacity to ae child ability valuable for the killed ector. Having aumed it i unbiaed, the prior aement about the child value on the killed labour market i θ. A Parent unconditional expectation about hi child abilitie i therefore: σ ε () E [ α ] = θ Sending the child to chool provide a ignal on hi ability level (3) z t = α + t Where t follow a normal ditribution with mean 0 9 and variance. The preciion / σ can be interpreted a a quality index for the aement proce at chool. At time t= the chool aement of the child ability i revealed a z = α +. The parent oberve it and make hi firt deciion about the child career: either he i withdrawn from chool or σ 8 An unbiaed ignal i not necearily a very realitic aumption ( even a beetle i a beautiful to hi mother a the Neapolitan aying goe) however it remove iue to do with inefficient chooling deciion and the dynatic egregation of job baed upon ocial confidence by the upper clae. A we will ee, the model already allow for the role of cultural bia in education deciion even with an unbiaed ignal: if the parent i a killed worker, he i likely to have a low and therefore attribute relatively more weight to hi own aement than to chool grading than a (le educated) parent with high leading to the reult that killed parent are le likely to withdraw their children from chool conditional on a bad σ ε grade. 9 Again, we do not conider another important ource of egregation into occupation, i.e. the impact of cultural homogeneity among killed familie and chool teacher on education choice. σ ε

15 i allowed to continue in education. The perceived benefit from continuing in education are meaured by the conditional expectation of the child ability : ˆ + ˆ (4) α t w where α t+ = E[ α I ] t Thi i a meaure of the expected wage in the killed labour market a a function of the etimated ability of the child conditional on the parent information et. Specifically information et at time t including all the ignal received until then. In the firt period, I t i the parent { θ } I =, z. The benefit of withdrawing the child from the chool are given by the expected wage on the labour market plu the option value of returning to chool next period. At time t= further information i releaed to parent. If the child wa thufar in chool, a econd ignal about her ability in the killed ector z = α + i revealed and a deciion about her future i made: either he continue her path toward the killed labour market (by entering univerity) or he return to the unkilled labour market. Benefit from continuation are therefore meaured by (5) ˆ α = E[ α ] 3 I The information et after two period in chool i I { θ, z z } =., If the child i withdrawn from chool after the firt period, he pend a period out of chool (ay working), a ignal i collected about the child opportunitie in the unkilled labour market. Define u (6) w t = w 0 + ut the child expected wage in the unkilled labour market. Where child potential wage in that market and the parent). u follow a normal ditribution with mean 0 and variance u w t i the parent prior belief on the i the pecific talent of the child in thi job (unoberved by. The parent doe not oberve, but an unbiaed ignal of child opportunitie in the unkilled labour market (ay the child current wage provided he i paid one), defined a u 0 w σ u (7) φ u t = w + δ t 3

16 where δ t follow a normal ditribution with mean 0 and variance period in chool and one period out of chool i then { θ, z φ } I D =., σ δ. The information et after one Summarizing, we model the period of adolecence a a learning proce by parent about their children abilitie and opportunitie in the preence of ome degree of irreveribility of educational choice. Parent make equential deciion about their child educational career baed on their attainment and grade. We will how that a good ignal at chool ( z ) on the child ability α zt increae parental expectation about what the child utility will be a a killed worker and will increae the chance that the parent will keep financing the child education. If thi ignal i relatively bad the parent will try the unkilled labour market where a ignal about the child opportunitie will be collected ( φ t ). If thi latter ignal alo turn out to be bad, the parent may be willing to reconider hi choice and enrol the child again at chool. All of thi i quite intuitive, the advantage of making the model explicit i to derive precie prediction about educational choice a a function of the parameter of the problem, i.e. the prior, the average kill premium in the market, the opportunity cot of children education for the familie and the preciion of different ignal about abilitie and market opportunitie. Notice that, a imple a the model i, it can allow for economic and cultural heterogeneity at the family level. Economic heterogeneity i captured by the opportunity cot faced by parent who bear the full direct cot of education, T. Cultural heterogeneity i caught by the preciion of the ignal the parent ha on their child ability in the killed ector and in the unkilled ector. The time line, the evolution of σ ε information et and the deciion tree i ummarized in the following figure: σ δ univerity ˆ complete education E[ α3 T I] I no univerity u E[ w3 I ] firt period in chool θ I complete education E[ ˆ α3 T ] drop-out from chool I D I tay unkilled u D E[ w3 I ] t t o t t3 Figure : Parental choice 4

17 3. Updating information about the child abilitie and opportunitie The updating formula are iteration on the conditional expectation operator where conditioning occur on the ignal recovered (thi i a verion of the Kalman Filter, ee Sargent 987, pp.30-3). Define the optimal weight parent attribute to ignal from chool a Σt (8) K t = Σ + σ t Where Σ ( ˆ t = E α α t ), therefore the updating formula on the child ability during hi chool career under the aumption of the preent model i given by (9) ˆ α t = ( K t ) ˆ αt + Ktzt Notice that K i a meaure for the relative preciion of the ignal at chool relative to the preciion of the ignal that parent collect on their own. Define the weight parent give to the ignal about their child opportunity in the unkilled labour market a σ u (0) H = σ + u σ δ Notice that H i a meaure for the relative preciion of the ignal in the unkilled labour market relative to the preciion of the ignal that parent have on their child opportunitie on the unkilled labour market. Notice that, ince the child can only re-enter after one period out of chool, we do not need iterative formula for updating ignal on the unkilled labour market opportunitie. Therefore the formula for the expected wage in the unkilled labour market i given by () w ˆ = E[ wφ ] = ( H ) w0 + Hφ. 5

18 We are able now to compute expected benefit in both ector conditional on the relevant information et. Conider the expected productivity in the killed ector after one year at chool when the core i obtained : z () ˆ α = ( K ) ˆ α + K z = ( K ) θ + K z 0 Where, ˆ α 0 = θ, 0 = σ ε and σ =. ε Σ K σ ε + σ After two year of chooling, expected productivity in the killed ector will be given by (3) ˆ α = ( K ˆ ) α + Kz Where Σ ˆ = E[ α α] = ( K) σ + ε K σ and K Σ = Σ + σ. After one (compulory) period at chool the expected wage in the unkilled ector will be given the unconditional expectation productivity in the unkilled wage i given by w 0. After one period at chool and one period out of chool, expected (4) w ˆ = E[ wφ ] = ( H ) w0 + Hφ Having defined the information updating proce for the deciion maker we can olve now for the equilibrium choice. 3. Equilibrium deciion making about children career Thi i a equential parental choice model about educational career of children. Choice at each point in time i made optimally, in the light of the current information et and given choice made in the pat. An equilibrium of the deciion making problem will be a et of threhold for the core obtained at chool and for the ignal obtained conditional on dropping out defining, in period, the choice to withdraw the child from chool and, in period, to enrol or not in the univerity conditional on being at 6

19 chool and to re-enter or not education provided one period wa pent out of chool. To obtain equilibrium deciion we work backward from the final period. After two period at chool the child, by now a young woman, ha produced two ignal z and z about her productivity in the killed labour market and no ignal on the unkilled labour market. Therefore 0 a univerity career will be choen if (5) ˆ α 3 w T conditional expected productivity in the killed labor market net of tuition fee w0 443 unconditional expected productivity in the unkilled labor market After ome trivial algebra thi can be written a (6) ( K )( K) θ + K( K ) z + K z wo + T w Which give the cut off value of z, ~ z ( z ) uch that, for any value of z conitent with continuation, if z > ~ z ( ) a univerity career leading to a killed job will be choen i.e. (7) z z ~ w0 + T ( K )( K) θ K( z (.) = K w K ) z. Thi characterize family deciion in the third period a a function of the hitory of core at chool, their relative preciion and other parameter of the model. After the firt period of chooling, i.e. conditioning on alone, with no dicounting, the net benefit from continuation at chool have to be traded off againt benefit from witching to the alternative of dropping out. In the Appendix, uing the iterated expectation law, we how that the choice of dropping out reduce to the following inequality z (8) E [ ˆ α I] w T conditional expected productivity in the killed labor market net of tuition fee w0 443 unconditional expected productivity in the unkilled labor market That i: (9) [ K ( K )] θ + K( K ) z w + T w 0 0 Remember that after completing high chool we aume that the choice between univerity and unkilled labour market become irreverible. Thi hypothei i made mainly to implify the model and i equivalent to make the cot of witching back to education after a certain age ufficiently large. However, the idea that irreveribility of choice about occupational career i a realitic feature of the model. A le dratic aumption would give a longer horizon to agent maintaining the option to go back and forth different education choice for a larger number of period at increaing cot, until it i no more worthwhile to gather information about different alternative. 7

20 Therefore a parent will chooe to have the child to continue in chool for the econd period if the ignal in the firt period i good enough (0) ~ w (.) 0 + T z z = K ( K ) w [ ( K) K] θ K ( K ) and drop out otherwie. Thi characterize family deciion a a function of firt period ignal at chool. Finally we need to characterize the deciion about re-entering chool after one period out. To thi end we define the expected benefit for continuing in the unkilled labour market conditional on two ignal: φ ( z i aumed to be irrelevant to review prior about child ability in the unkilled labour market) and the expected benefit from re-entry conditioning on z alone (ince φ i aumed to be irrelevant to ae opportunitie in the killed labour market). The latter i equal to the left hand ide of equation (8). The former i given by: () V R = ( H ) w0 + Hφ Therefore re-entry will occur if and only if () ( H ) w0 + Hφ {[ K( K)] θ + K( K) z} w T i.e. (3) {[ K ( K )] θ + K ( K ) z } ~ w T ( H ) w φ φ(.) = H 0 At equilibrium, conditional on having dropped out of chool, the probability of re-entry i negatively related to the ignal parent obtain about the child opportunitie in the unkilled labour market. The intuition for the reult i quite traightforward: the child i given a econd chance at chool if the ignal about alternative opportunitie i even wore than the ignal obtained at chool. What i of interet for the empirical part i the analyi of the determinant of the threhold in equation (0) and (3). 8

21 3.3 Comparative tatic and prediction for the empirical reult The main concluion we draw from the theoretical framework decribed in the preent ection i that during chool familie learn about their child talent in alternative occupation and react to thi information through the choice of educational invetment. We identify a et of parameter that characterize the family ocio-economic tatu a an important determinant of drop-out behaviour. The model alo how that there i the poibility that a parent may rationally decide to have hi child return to chool after pending a period outide a a reaction to new information about hi kid talent. The next ection will invetigate whether thi i empirically relevant and whether the determinant of dropping out and re-entry reflect the determinant highlighted in the model we preented. Importantly for the dicuion of our empirical reult we conider the comparative tatic for the equilibrium threhold for dropping out of chool and the equilibrium threhold for re-entry. Reult can be tated about the effect of the relative preciion of the ignal in the parent information et, providing ome characterization of the effect of cultural heterogeneity on educational choice. Dropping out after the firt period ignal wa characterized by the threhold ~ z (.) defined in eq. (0). By uing the definition for and K, thi latter expreion can be rewritten a: K (4) ~ w0 + T σ w + T (.) ( )( 0 z = + + θ ) w σ w ε We immediately obtain the following comparative tatic reult: ~ z ~ ~ ~ (.) z (.) z (.) z (.) (5) < 0, > 0, > 0, < 0. w w T θ 0 A larger perceived kill premium (larger or lower w ) intuitively make familie choice le w 0 elective, reducing the threhold and allowing their kid to continue even in the face of a bad chool ignal. Larger educational cot make familie more elective and increae the probability of T Though intuitive, thi reult i intereting: raiing trend (a recently oberved in Oecd countrie) in the kill premium induce familie to be more puhy in the career choice of their kid diluting talent allocation in the killed ector, ee D Amato and Mookherjee, (007). 9

22 chool abandonment. A larger θ i.e. a better prior about the child talent in the killed ector make familie le elective and reduce the probability of dropping out. Thoe reult are quite intuitive and will be ued extenively in the interpretation of our empirical reult. More ubtle and intereting iue arie when it come to the reult about σ ε and σ. Remember that σ ε i the (invere) preciion of the family in aeing the kid talent and perpective in the killed labour market, wherea σ i the (invere) preciion parent attach on the chool grading proce in the aement of the ame index. σ Define ρ = a a meaure for the relative weight parent aign to the firt period ignal at chool, σ ε given the option to recover a econd ignal at chool relative to the prior. It i a meaure of the cultural confidence parent have in making their deciion baed on the public aement at chool relative to their private aement. We obtain ~ z + (5) (.) w0 T = θ ρ w Therefore the derivative above i igned according to the ign of w 0 + T θw, i.e. the effect of the relative preciion of the ignal depend on parameter value. To interpret the reult above notice that w0 + T < θw implie that from the point of view of the family it i ex-ante efficient to end the child to chool (remember that θ i an unbiaed etimate of α ). A a conequence the model predict that, ceteri paribu (i.e. with given perceived kill premium and opportunity cot of education), familie with larger cultural capacity (larger ρ ) will be le elective with repect to kid for whom education i ex ante efficient (aement baed on θ ). In other word dropping-out from chool i le likely to occur in more educated familie, conditional on the kid talent being ex-ante aeed valuable for a killed occupation 3. Alo notice that for given θ and perceived kill premium, the larger the cot of education, the more elective i the family. 4 With rik neutrality ending the child to chool i ex-ante efficient when, conditioning on the prior information θ, the expected return of education i above it opportunity cot (equal to the um of direct education cot and foregone return in the alternative occupation). 3 One implication of the model i that le precie chool ignal (larger σ ) make familie le trict and dilute the average ability level of kid continuing in education. 4 It i important to note that in a more imperfect (le intergenerationally mobile) world than the one conidered in thi model, children in educated familie would have better perpective in the killed ector, ex ante and independently of their chool attainment, due for example to inheritance of (killed) job. In term of our model we can capture thi effect by 0

23 Therefore both the quality of the public ignal (lower quality of the grading proce at chool z) and the private one (quality of the parental aement θ ) affect drop-out rate. Summarizing, the implication of the model for our empirical pecification of the probability of dropping out of chool i that both the impact of chool quality and the impact of parental cultural capacity ha a non linear effect on drop-out rate, interetingly the model capture different channel through which the family cultural capacity and the family economic capacity influence the education invetment deciion. Thi feature allow u to introduce parental education and meaure of familie permanent income a eparate determinant of the invetment choice. The deciion to re-enter after a period out of chool wa characterized by the threhold in eq. (3). Straightforward algebra how that ~ ~ ~ ~ φ (.) φ(.) φ(.) φ(.) (6) < 0, < 0, > 0, > 0. w T θ z 0 In word, re-entry i le likely when the family expect the child to face better opportunitie in the unkilled labour market (larger w ) and/or larger cot of education (larger T ). A larger prior about 0 the child opportunitie on the killed market ( θ ) and a better grade z in the firt period at chool increae the probability of re-entry. Moreover, children from richer familie are more likely to re-enter conditional on drop-out. Thi concluion i reinforced when we conider the comparative tatic with repect to the preciion ~ φ (.) of the ignal. To compute rewrite equation (3) uing the definition of ~ z from equation (0), H we get: ~ K K (6) w z ~ ( ) z ) φ (.) = 0 + ( w H evaluated at z ~ (.). Since H doe not enter into (0) we get z ~ φ (.) (7) > 0 H noticing that in more educated familie, children would tart their chool career with a larger θ : the effect of cultural capacity would reinforce the tandard economic argument baed on wealth contraint: the ign of equation (5) i more likely to be negative in more educated familie, i.e. given z children in more educated familie would be le likely to drop out.

24 Remember that from equation (0), H meaure the relative weight placed on the ignal received about opportunitie on the unkilled labour market relative to the weight placed on the prior by each family. To derive empirical prediction from thi latter comparative tatic reult conider that in the cae of opportunitie in the unkilled market, the weight put on the prior (relative to a ignal) i likely to be larger for a parent working in the unkilled ector: there i le to learn about the unkilled opportunitie facing hi child for an unkilled worker than for a killed one. We can conclude that, conditional on chool abandonment, the probability of re-entry i larger for killed familie than for unkilled one. In a pecific ene the link between parental tatu and children educational choice exhibit peritence driven not only by wealth contraint and financial market imperfection (larger cot of education in le well to do familie) but alo by the cultural and ocial ability of different familie to proce ignal about their children abilitie in two alternative occupation 5. Summarizing, in thi ection we have laid out a imple model of parental deciion making about educational choice when the proce involve learning about the child abilitie and job opportunitie in two alternative occupation (killed and unkilled). The model how that cultural capacity and economic tatu of the family affect the probability of being a drop out, along with traditional determinant uch a the kill premium a perceived by the deciion maker. In adherence with the aim of the empirical analyi the model alo how that conditional on being a drop out the probability of returning back to chool i affected by the ame variable in an intuitive way. With thi theoretical framework in mind we now move to the empirical analyi. 5 A already noticed thi doe not mean that peritence i rooted on efficiency ground in our model. Of coure, along with financial market imperfection, cultural bia and other form of intergenerational peritence of job allocation may have important ocial cot when we conider the problem of allocating talent to job. We do not addre thi point here.

25 4. Empirical Analyi: data and decriptive tatitic On the bai of the theoretical model and general conideration offered on the likely caue of dropping out behaviour offered above, in thi ection we report the reult of etimating an empirical model of chool-leaving and permanent dropping out behaviour amongt young people from Salerno and province. Data ued in our analyi are drawn from a urvey carried out in 004 by CELPE (Centro Interdipartimentale di Economia del Lavoro e di Politica Economica, Univerity of Salerno) on behalf of the Province of Salerno, and upplemented in 005. The aim wa to better undertand the magnitude and determinant of the upper econdary chool dropout phenomenon in the province of Salerno of thoe aged 5-8. Table 4 report ome information, provided by the local CSA (Centro per i Servizi Amminitrativi di Salerno), on the ditribution of enrollment in the high econdary public chool in the Province during the chooling year Table 4: Number of enrolled in the chool and tudent interviewed in the urvey Type of chool Number of enrolled Enrolled(%) Number of chool in the ample Number of tudent interviewed Scientific Vocational Technical- commercial Technical- indutrial Claical Pycho-pedagogical Other (ITG,LL,IA) Total Source: Data provided by CSA of Salerno We contructed our ample on the bai of thi ditribution. A regard tudent regularly attending chool, we employed a two tage procedure in which firt we extracted of the total of 85 chool in the province taking into account the ditribution of chool acro geographical area and chool type. Secondly around 600 tudent were randomly drawn from the chool record. A regard the dropout (and returnee) in our ample, a lit of name of peron identified a dropout by chool wa provided by the local CSA and contained information on around 900 3