Social Mobility: What is it and why does it matter? Sebastian Galiani

Transcription

1 C E D L A S Cenro de Esudios Disribuivos, Laborales y Sociales Maesría en Economía Universidad Nacional de La Plaa Social Mobiliy: Wha is i and why does i maer? Sebasian Galiani Documeno de Trabajo Nro. 101 Junio, 2010 ISSN

2 Social Mobiliy: Wha is i and why does i maer? 1 Sebasian Galiani Washingon Universiy in S. Louis April 2007 Draf Version 1 Documen elaboraed for he 7 h Social Equiy Forum, IADB. I hank he excellen research assisance of Maria Eugenia Gariboi.

3 INTRODUCTION The definiion of social mobiliy is he objec of some discussion, and alhough here is a common hread ha runs hrough all of hese discussions, he acual definiion varies from sudy o sudy. There is agreemen ha social mobiliy refers o movemens by specific eniies beween periods in socioeconomic saus indicaors (Behrman, 2000) and ha i aims o quanify he movemen of given [eniies] hrough he disribuion of economic well-being over ime, esablishing how dependen one s curren economic posiion is on one s pas posiion, and relaing people s mobiliy experiences o he overall condiions of he economy in which hey operae (Fields, 2000). Differences arise, however, when an aemp is made o endow hese definiions wih empirical conen (i.e., when an effor is made o deermine wha variable should be used o measure mobiliy, wha exacly should be considered movemen in a disribuion, or wha ime spans should be used o evaluae mobiliy). In he following discussion, we briefly commen on some of he concepual issues ha have been raised in he lieraure on mobiliy. Among he muliple consideraions concerning he definiion of mobiliy, in his paper we define social mobiliy as a siuaion in which he relaive economic saus of an agen is no dependen on saring condiions such as parenal income or family background. Therefore, analyzing he deerminans of mobiliy involves exploring he channels hrough which offspring s income is correlaed o is parens, such as inheried beques, educaion, formal rules, skills, opporuniies, working spiri, among many ohers. As parenal linkage is a source of differences in income among individuals, here is a deep relaion beween social mobiliy and inequaliy. They are joinly deermined, and he mos prevalen heoreical associaion beween mobiliy and inequaliy is negaive; since srucural condiions ha lead o low mobiliy also end o favor unequal oucomes. Assessing inequaliy, leads as o invesigae analyical frameworks o analyze he sources of differences in incomes: from effor, educaion and abiliy o he beliefs abou he naure of he income generaing process. As long as hese deerminans are a leas parially relaed o he parenal background, we will find a srong link beween social mobiliy and: equal opporuniies, meriocracy, human capial accumulaion, poliicoeconomic consideraions and beliefs, which we will accoun for in his survey. Furhermore, when iniial condiions preven individuals from allocaing resources opimally, if social mobiliy is limied, economic efficiency is reduced. For example, his happens whenever liquidiy consrains preven individuals from acquiring an efficien level of human capia. Therefore, i is of grea relevance o undersand ha social mobiliy and efficiency are also deermined ogeher. 1

4 Finally, hroughou his survey, we map he key parameers affecing mobiliy ino proposed policy acions, from each model sudied. We find ha policies ha break he dependence of oucomes on iniial condiions, such us universal public educaion or early inervenion programs may be successful in raising income and social mobiliy. Furhermore, due o he relaionship beween mobiliy and oher social and economic dimension such as efficiency and inequaliy; hose policies can have broader shor and long erm effecs. This survey is divided ino 8 secions. In he firs one, some preliminary conceps relaed o he definiion of mobiliy are briefly explained. Secion 2 comprises he review of a range of models of income mobiliy ha relaes i o human capial, credi consrains, educaion and echnology, among ohers. The hird secion deals wih he poliicoeconomic consideraions regarding inequaliy and mobiliy. In Secion 4, i is esablished he relaionship beween social mobiliy and boh equal opporuniy and meriocracy. The nex secion inroduces a key concep: efficiency, in he conex of he models ha assess social mobiliy. In secion 6, here is a discussion abou he effecs of social mobiliy from an economic efficiency and also from poliical oucomes poins of view. Secion 7 includes models ha consider he percepion of mobiliy. To conclude, in secion 8, here is a summary of he policy implicaions of he surveyed models, showing he differen policies ha have he poenial o improve social mobiliy in he shor and long erms. 2

5 1. PRELIMINARY CONCEPTS Socioeconomic Saus Indicaors When sudying mobiliy, we are ineresed in using an indicaor ha can capure some elemen of economic well-being. This enails aking variables ino consideraion which measure long-erm saus raher han shor-erm flucuaions. (We do no, afer all, wan o confuse social mobiliy wih economic insecuriy.) When rying o encapsulae his general idea of concree, operaional conen, we may wan o consider consumpion (which is, presumably, closely linked o permanen income), educaional aainmen, asse holdings (wealh), or some composie measure of socioeconomic level. Daa availabiliy consideraions, unforunaely, quickly limi he scope of he indicaors used in acual sudies, as mobiliy research calls for long panels, or, a he leas, informaion on parens and offspring. I is already quie hard o find high-qualiy daases ha provide his kind of informaion on income and labor earnings, which are some of he mos commonly measured socioeconomic indicaors. Reliable long-erm informaion on consumpion, or socioeconomic saus, is pracically nonexisen, especially in developing counries. Daa on inergeneraional educaional aainmen, on he oher hand, is easier o find, parly because rerospecive quesions (quesions on parenal educaional aainmen, for insance) are bound o be reliably answered. As a resul, mos of he sudies now available focus on income and educaional aainmen. Time Period There are wo main ypes of mobiliy ha we may wan o sudy, depending on he lengh of ime we allow for changes o ake place. Inrageneraional mobiliy refers o movemens in he indicaor of choice ha occur in a relaively shor ime span ypically wihin an individual s adulhood. Inergeneraional mobiliy, on he oher hand, refers o changes ha are observed from one generaion o he nex. Thus, inrageneraional mobiliy sudies follow individuals hroughou heir lives, while inergeneraional sudies focus on enire dynasies, racking heir movemens from one generaion o he nex. Movemens The main source of conroversy regarding social mobiliy is arguably he issue of how o define movemen wihin a disribuion. Differen concerns give rise o very differen ideas abou how o quanify changes in an individual s economic saus. A very preliminary observaion is ha no meaningful movemen can ever occur unless here is variabiliy in he values of he indicaor o be sudied. In oher words, income mobiliy would be an empy concep if income inequaliy did no maer. Fields (2000) provides a useful caegorizaion of differen mobiliy conceps, as well as saing some of he implici assumpions and value judgmens underlying each one. He shows ha he kind of normaive (or subjecive) choice ha is made in sudies of social mobiliy goes beyond simply deciding wheher i is a good or bad feaure. Following 3

6 Fields (2000), imagine he following socieies numbered from 1 o 5, formed by 3 individuals (hese are somewha exreme examples, bu serve o poin ou he sources of disagreemen): Table 1: Hypoheical Changes in Income Disribuions Andrea Brian Chris Any relaive measure of mobiliy would indicae ha, in going from sociey 1 o sociey 2, here has been perfec mobiliy. The correlaion beween he wo, indeed, is zero. Bu noe ha average wealh has gone down and, as a resul, so have income levels for all bu one of he individuals. The ransiion from sociey 2 o sociey 3, where he correlaion is 0.5 mobiliy is much lower bu all incomes have gone up, is he mirror image of he firs. In his sense, i could be argued ha he movemen from 2 o 3 is more desirable han from 1 o 2. The main poin here is ha relaive measures of mobiliy do no ake changes in he average income level ino accoun. While his is seen as a flaw by researchers who would say ha an environmen where all incomes are growing is mobile or dynamic, even if social ranks are no moving, we believe ha mobiliy concerns arise mainly because of relaive consideraions. In oher words, socieies end o favor siuaions where individuals relaive saus is considerably independen from heir parens degree of success, and his is bes capured by measures of relaive mobiliy. One disincion should be noed wih regard o measures of relaive mobiliy. Posiional movemen akes place when an individual changes her posiion in he overall disribuion. Relaed o his is share movemen, which focuses on he change in an individual s share of he overall oal. 2 Boh are insances of wha Behrman (2000) calls relaive or exchange mobiliy. A process whereby all members double heir incomes would be perfecly immobile under boh measures (his would correspond o going from sociey 1 o sociey 4). Also, a process in which oal income decreases and inequaliy increases while ranks remain he same would show no posiional mobiliy, bu shares would have changed (his is he case in going from disribuion 4 o 5). Rankings can also change drasically wih very lile change in income, as is he case in he shif from sociey 2 o sociey Alhough we are rying o avoid referring o income in order o drive home he poin ha we are ineresed in a broader noion of social mobiliy, i is clear ha here mus be some quaniaive elemen in order o alk meaningfully abou shares. 3 This kind of objecion is valid o some exen, and we menion i because some of he researchers in his area acually do raise such objecions. Bu he fac is ha his kind of example does no seem o be in line wih wha we see or would expec o see in real life seings. And relaive movemens do have he advanage ha hey capure he persisence of inequaliy in a way ha absolue measures do no precisely because hey absrac away from changes in mean income, or even in is disribuion. The main poin o be 4

7 The aim is o isolae he disribuional componen from mobiliy. We believe ha mobiliy concerns are enirely relaed o ranks; hus, here may be social mobiliy even if he overall disribuion becomes more unequal. In any case, he lesson o be learned from hese examples is ha a complee picure of he desirabiliy of an income process canno be derived from any one summary measure because changes in average income levels, changes in he overall disribuion, and he degree o which relaive performance in one generaion depends on relaive performance in he pas mus all be aken ino accoun. Absolue movemen measures, in conras, focus on quanifying he oal change, regardless of wheher any exchange mobiliy has aken place. We will no go ino deailed definiions of hese insrumens here, however, since hey do no seem o be relevan o he ype of concern ha drives his sudy. Alhough we may be conen wih quanifying movemen whaever definiion we decide upon i is usually he case ha we also wan o capure oher aspecs of movemen. In paricular, sudies of social mobiliy are generally concerned wih gauging how dependen final oucomes are on iniial condiions. In oher words, income mobiliy may exis because individual incomes follow an idenical random process, independen of iniial income, or here may be some sor of dependence usually capured by a correlaion coefficien beween income realizaions for he same individual (or dynasy) across ime. Mos sudies of mobiliy equae ime dependence wih immobiliy and, generally speaking, his is he approach ha is favored in his paper. We believe ha he concep of mobiliy is quie disinc from ha of economic growh and is closely conneced o noions of efficiency, fairness, and poliical conflic which follow pahs ha are largely unconneced o overall growh. This is why we choose o focus on measures of relaive, raher han absolue, mobiliy. As will be made clear in his paper, he ime span o be chosen will depend on he conex of he analysis, while he issue of ime dependence will invariably play an imporan role: increasing social mobiliy implies breaking he dependence of individual economic oucomes on iniial condiions. Normaive Analysis of he Correlaion Coefficien A low correlaion coefficien indicaes ha mobiliy is high and ha parenal income is weakly correlaed wih individual income, whereas a high correlaion coefficien signals low mobiliy. However, auhors such as Swif (2005) and Feldman e al. (2000) claim ha a zero correlaion is no a morally desirable goal because any serious aemp o disconnec he life-income of parens and heir offspring would severely compromise imporan values of family life and privacy. Thus, hey argue, insead of pursuing he objecive of zero inergeneraional correlaion, we should ask ourselves which mechanisms of inergeneraional ransmission are unfair and should hen design our made here is ha, jus as reporing on inequaliy does no seem complee wihou sudying mobiliy, measuring mobiliy will no give us a perfec picure of how desirable a given sociey is. Alhough his is undeniably he case, i is also rue of any oher one-dimensional measure. 5

8 policies accordingly. Following he same line of reasoning, Jencks and Tach (2005) claim ha if we wan o know wheher opporuniy is becoming more or less equal, we need o rack inergeneraional linkages ha violae cerain norms associaed wih meriocracies and developmenal opporuniy. Under heir definiion of developmenal opporuniy, sociey mus eiher make families and communiies more alike or find ways o offse he adverse effec of growing up in a disadvanaged family or communiy. Implici in he reasoning of hese auhors is he idea ha some sources of advanages are accepable or even desirable while ohers no. For insance, many people agree ha ehniciy should no be a source of advanage, bu ha effor should. Family conacs, inelligence, or oher geneic or environmenal rais are more debaable. Therefore, if accepable sources of advanages are somehow inheried by children of advanaged parens, we would observe a posiive correlaion beween parenal and individual incomes even if no unaccepable source of advanages remained. However, even if all sources of unaccepable advanages were eliminaed and he correlaion beween parenal and individual income were fully explained by accepable advanages, we could sill argue ha policy inervenions o help he disadvanaged would reduce he correlaion. Normaive evaluaion of such policies would ulimaely depend on he social preferences of he evaluaor and his preference for mobiliy per se. Relaion wih Oher Disribuional Feaures Concerns abou saic aspecs of a sociey s welfare disribuion such as inequaliy, povery or polarizaion are, as a rule, inimaely conneced wih any discussion on social mobiliy. Mos heoreical sudies focus on he join deerminaion of mobiliy and inequaliy, since conceps such as povery and polarizaion are hard o incorporae ino a model. We will herefore examine he relaionships beween inequaliy and mobiliy. The mos common characerizaion poins o inequaliy as being a snapsho of he income-generaing process a any poin in ime, while mobiliy is seen as racking income disribuion over ime based on individual rajecories. When considered from his sandpoin, he absence of mobiliy accenuaes all issues associaed wih inequaliy. I also underscores he fac ha a comparison beween he prevailing income disribuions in wo socieies wo snapshos may reverse when mobiliy is incorporaed ino he analysis. This reversal would only happen if higher mobiliy were somehow associaed wih higher inequaliy and vice versa, so ha superficially equal socieies migh acually have more persisen inequaliy han highly unequal socieies. As we will see, his is far from obvious, and heoreical models as well as empirical evidence provide mixed resuls. In fac, he mos prevalen heoreical associaion beween mobiliy and inequaliy is negaive, since srucural condiions ha lead o low mobiliy also end o favor unequal oucomes. 2. MODELS OF INCOME MOBILITY 6

9 Becker and Tomes (1979) were one of he firs o model income mobiliy and inequaliy. In heir economy, here is a coninuum of dynasies. Each generaion values is own consumpion as well as is offspring s income:, I1 U U Z (1) where U is parens uiliy, Z sands for parens consumpion, and I +1 is he adul wealh of heir children. This wealh is embodied in a sock of human and nonhuman capial ha has hree sources: a direc invesmen from each generaion s parens (y); endowed luck ha is correlaed across coniguous generaions of he same dynasy (e) (which can be inerpreed as abiliy, inelligence, social background or values, and family connecions); and sheer marke luck (u). I w y w e w u (2) In oher words, we hink of individuals in his model as helping heir children ou in wo ways. They can decide o leave hem capial by invesing in heir educaion or providing hem wih financial capial. This is a deliberae decision on he par of he parens. In addiion, hey pass on family characerisics ha were assigned by luck o each dynasy. Parens canno aler such characerisics or preven hem from being ransmied. A naural inerpreaion would involve geneic characerisics, bu here are also family connecions, norms or cusoms wihin each household, as well as oher non-biological rais, ha are largely he resul of each family s hisory and ha canno be radically changed by any individual dynasy. A poor paren canno build family connecions ou of hin air. Of course, here is a final elemen of luck in deermining individual income; people will ypically differ in he exen o which hey ake full advanage of heir endowmen, and heir resourcefulness or drive may lead hem o find new opporuniies. Serendipiy may also inervene. This is he way in which he erm u should be inerpreed. As can be seen from equaion (2), each par of his capial sock has he same (consan) marke reurn, w. 4 Parens are assumed o be risk-neural and o choose heir bequess in order o maximize heir own expeced uiliy, subjec o a budge consrain (where r is he inergeneraional rae of reurn), w y Z 1 r 1 1 I (3) 4 Thus, boh inequaliy and mobiliy refer o he disribuion of capial sock or of all sources of income. 7

10 and a law of moion for endowed luck ha depends on he family endowmen and he average level of endowed luck in he economy. 1 1 e 1 h f e he v (4) In his law of moion, h represens he fracion of family endowmen ha is inheried, and f is he aggregae rae of growh, while v is a random shock. We hus allow for slow changes in family luck. I may be he case ha a rich family loses par of is connecions, or ha someone from a family ha does no value hard work may sill urn ou o be hardworking and pass his rai on o his children. In any case, as we will see, h is a very imporan parameer of he model, as i measures he exen o which family luck is equalized across dynasies. When h is close o 0, family endowmens are basically idenical, wih some random variaion. When i is close o 1, dynasies differ permanenly. Families fully anicipae inheried endowmen (presumably, any relevan random shocks o abiliy, personaliy, or he like can be observed before making he opimal invesmens), bu no random luck. From sandard expeced uiliy maximizaion, and normalizing r and w o equal 1, he income of children in he +1 generaion of he ih family can be expressed as: I a I he v u (5) i i i i i Using Table 2, equaion (5) says ha income in a given generaion basically depends on parenal wealh and endowmens, alhough an addiional effec is generaed hrough endowed and marke luck. Crucially, parenal preferences deermine how srong his dependence is. This model capures he fac ha anicipaed luck affecs how much capial parens leave o heir offspring, which is why boh marke and endowmen luck are no fully appropriaed by heir children (hey only ge o enjoy a proporion ). Table 2: Key Variables in Becker and Tomes (1979) Variable Inerpreaion/Definiion Depends on Proporion of parens wealh ha goes o children s income Acual value of he propensiy o inves in children - Parens uiliy funcion specifically, how much children s income affecs parenal welfare - Inergeneraional rae of reurn. = 1 r a Baseline endowed abiliy e1 h All families are assumed o be idenical. This means income inequaliy depends on he pas hisory of marke luck. Assuming ha parameers are such ha he persisence of iniial condiions is limied (, h 1), income in generaion +1 is: 8

11 a h I u v 1 1 h k1 k1 i k i i 1 1 k 1 k k0 k0 h (6) and he (squared) coefficien of he variaion in income a measure of inequaliy 5 is: 1h1 h 1 CV CV CV I u e (7) Tha is, inequaliy has wo componens: one ha comes from marke luck (u), and one ha comes from endowed advanages (e). 6 Clearly, if any of hese componens were less variable, income inequaliy would go down. The addiional insigh derived from his model comes hrough he effecs of and h. Noe ha he coefficien for endowed family luck is larger han he coefficien for marke luck. The difference beween hem grows as and h become larger. Tha is, as we increase he acual value of he propensiy of each generaion o inves in he nex and he degree of family inheriabiliy of characerisics ha affec income, we give greaer weigh in overall inequaliy o family-specific advanages. However, whereas an increase in h unambiguously increases inequaliy, an increase in say, as he resul of a change in preferences or hrough an increase in marke reurns reduces he coefficien of variaion in income. This is he resul of he fac ha, while i increases he variance in income, i increases he level of income even more. We nex urn o income mobiliy and hen analyze how and h affec he rade-off beween inequaliy and mobiliy. The preferred measure of income mobiliy in his aricle is he effec of an increase in income for generaion on he incomes of subsequen generaions. This gives us an idea of how quickly emporary increases in social sanding fade away. I measures how long i akes o go from rags o riches and back. In oher words, i capures our preferred concep of mobiliy as he degree of dependence of curren oucomes on pas performance. Lower persisence is equivalen o higher mobiliy. 5 The coefficien of variaion of a random variable is defined as he raio of is sandard deviaion o is mean. Tha is, CV x /. In his case, v has zero mean, so ha is sandard deviaion is normalized x x by average endowed luck, or e. 6 The las erm acually reflecs exogenous variaion in endowed luck, since 2 e 1 h 2 v 2. 9

12 Table 3: Effecs of One-Time Changes in Income Behavioral and i Source of Change I m Parameric Assumpions Marke or endowed luck Endowmen Endowmen I h1 m i I m i h I m h h m e i e h negligible 1 No opimizaion invesmens are given Opimal behavior h 1 Opimal behavior h 1 As m Goes o Infiniy Declines monoonically Declines monoonically Rises up o a peak in a generaion ha depends on h, hen declines monoonically Declines monoonically This effec will depend on he source of he increase in income and, as he auhors show, is magniude hinges on he inerplay beween opimizing behavior and inheriabiliy. Indeed, if we call I a change in income for generaion, and we race changes in he mh generaion, we can envision he differen scenarios described in Table 3. When he degree of inheriabiliy of endowed luck is close o zero, a look a equaion 5 ells us ha each generaion will receive a fracion of any change in he income of he previous generaion, regardless of he source of his income. This change will decrease as he disance beween generaions increases, given our assumpion ha 1. In oher words, when families do no provide sizeable (dis)advanages o heir offspring, mobiliy is high. If inheriabiliy was high, bu invesmens were no influenced by changes in endowmens ha is, if families did no opimize we would see a similar response o a change in endowmen. However, if we ake ino accoun he fac ha families do opimize, we can see ha, for some parameer values, a change in family endowmen a ime can compound over ime before i fades away (implying ha a lucky generaion will make is descendans luckier han average for a relaively long ime). This is exacly he resul ha we would associae wih a lack of social mobiliy. We can now see how income inequaliy and social mobiliy may be negaively or posiively correlaed, depending on wha is driving heir movemens. When inergeneraional inheriabiliy of advanage increases, income inequaliy goes up and social mobiliy goes down. Thus, differences beween families are exacerbaed and made more persisen. 10

13 This is inuiive: if family connecions or race become more imporan in deermining individual income, we would expec differences beween families o become more pronounced and permanen. When he propensiy o inves in children goes up, mobiliy again is reduced, because a one-ime shock o income akes more ime o fade away. However, in he long run, income differences are reduced, so income inequaliy goes down. We can summarize hese findings in he following able. Table 4: Relaionship beween Inequaliy and Mobiliy when Parameer Values Change Effec of an Increase in Parameer Parameer Inerpreaion on Inequaliy on Mobiliy Parenal propensiy Reduces Inequaliy Reduces Mobiliy o inves in children Inheriabiliy of h Increases Inequaliy Reduces Mobiliy family advanage Clearly, is no a parameer ha can be manipulaed by public policy. I is quie impracical and, arguably, even unehical for he sae o ry o convince parens o care less (or more) for heir children s well-being. However, i is no implausible for aleraions in h o fall wihin he scope of public policy. Noe ha a decrease in h is equivalen o a homogenizaion of endowmens. Tha is, a decline in h makes endowmens more likely o equal he average. Hence, a policy ha, for example, calls for invesmens o be made in raising he qualiy of public educaion while making i more homogeneous 7 would probably redund in a decrease of h. Noe ha his reducion would also end o reduce inequaliy. Anoher way of changing h is by promoing meriocraic employmen policies, possibly hrough encouragemen of marke compeiion among poenial employers. Why would marke compeiion help aain a meriocracy? Advanages in he labor marke ha are no relaed o higher produciviy such as race or family connecions can only persis if companies ha engage in hese hiring pracices are shielded from heir consequences. Firms in a compeiive environmen, in conras, will come under pressure o adop pracices ha favor produciviy over personal loyalies or racial prejudice. The main claim underlying hese suggesions is ha policies ha break he dependence of oucomes on iniial condiions are unambiguously desirable. Becker and Tomes (1979) absrac from he deerminaion of he reurn o human capial, equaing i o physical capial and operaing wihin a saionary economy. Alhough he basic insigh ha mobiliy and inequaliy are affeced by he way in which parens opimize when making heir decisions, as well as by inheriance of personal qualiies is 7 And, poenially, more similar o educaion in privae schools. 11

14 no in dispue, some unbundling of he process of human capial accumulaion as an addiional force driving inequaliy and mobiliy remains o be done. We will commen on wo lines of work. One focuses on purely economic forces, while he second adds poliico-economic consideraions. Building on Becker and Tomes: Human Capial and Credi Consrains Hassler, Rodríguez Mora and Zeira (2003) and Owen and Weil (1998) show how inequaliy and mobiliy may be joinly deermined in a general equilibrium model wih overlapping generaions of workers. In boh cases, hey draw a disincion beween skilled and unskilled workers. They analyze mobiliy by deermining he odds ha he child of an uneducaed worker will become skilled (upward mobiliy), or he odds ha he child of a skilled worker will no receive an educaion (downward mobiliy). 8 The key issue in boh models is he lack of access o a credi marke, since such access would allow high-abiliy individuals o inves in heir educaion. This is a very pracical concern, inasmuch as i has he consequence of making educaional decisions (and, herefore, income) srongly dependen on parenal background. In oher words, i is a reinerpreaion of he parameer h in he Becker and Tomes (1979) model. Boh models assume ha abiliy is no geneically deermined. This is why credi marke failures end up accouning for mos of inefficien immobiliy. The key poin o bear in mind, hough, is ha his is a simplifying assumpion which serves o highligh wha aspecs oher han geneic endowmens may affec inergeneraional mobiliy. These effecs would persis even if abiliy were, o some degree, geneically inheried. Owen and Weil: Liquidiy Consrains and Muliple Equilibria Owen and Weil (1998) model he join deerminaion of aggregae oupu, income disribuion, mobiliy, and reurns o educaion in general equilibrium. Skilled and unskilled labors are complemens in producion, and changes in reurns o skill sem from changes in he aggregae supply of each kind of labor. 9 In oher words, a large supply of unskilled workers increases he skill premium, and vice versa. Agens differ across wo dimensions: hey receive differen parenal ransfers, and hey are born wih differen abiliy levels. Abiliy is independen across generaions and is defined as he amoun of efficiency unis supplied o he labor marke, regardless of skill level (which, insead, affecs he wage level a which hose unis are rewarded). Thus, abiliy is no geneically deermined and can be likened o indusriousness (i.e., how hardworking a person is). 8 Noe ha hese wo probabiliies may move in opposie direcions: a policy ha increases overall educaional achievemen may raise upward mobiliy and reduce downward mobiliy. Thus, we once again run ino he problem of clearly defining wha we wan o include in he definiion of mobiliy, or mus ask ourselves wheher bundling all hese phenomena ino one concep even makes sense. 9 Underlying his resul, here is a neoclassical producion funcion and perfec capial mobiliy, so he marginal produciviy of capial is consan. 12

15 The iming is as follows. Individuals can be said o live hrough wo sages. In he firs, hey receive ransfers from heir parens, hen choose an educaional level, and work. In he second, hey consume and leave a beques o heir children. i An individual can acquire skills by buying educaion a a fixed cos e. If we call q an s individual s abiliy level and w he wage for skill level s, hen we find ha here is an abiliy hreshold above which i pays o become educaed. 10 In an efficien oucome, individuals whose abiliy level exceeds his hreshold will obain an educaion. q e * e u w w (8) However, here are no credi markes available o finance educaional decisions. This means ha parenal bequess (x) are he only source of funding. Thus, individual resources are given by: x e q w if x e and q q e i i, i, i, u xi, qi, w oherwise * (9) In oher words, agens will receive an educaion only if heir bequess enable hem o afford i. Resources are spli beween individual consumpion and bequess o children, wih being he weigh ha is given by parens o bequess., ln ln 1 U x c x c (10) Clearly, in choosing a given beques level, parens are deermining he expeced value of heir children s educaion level. For insance, a beques lower han e ensures ha children will be unskilled workers. The opimal decisions of each family define, for each disribuion of labor supply and each level of wages, wha he ransfers and resuling educaion levels will be for he nex generaion. The auhors look for a seady sae of his model a relaive wage level and skill disribuion such ha: - Families expec wages o say he same and herefore choose ransfers in such a way ha he educaion disribuion remains unchanged; and - Given he educaion disribuion, his wage level is he oucome of marke equilibrium. 10 Equaion (8) also shows ha, in equilibrium, skilled wages mus be higher han unskilled wages. 13

16 In oher words, he saring poin for he siuaion is such ha he economy will remain in he same sae indefiniely. Owen and Weil find ha when individuals face liquidiy consrains, here are muliple seady-sae equilibria which exhibi a posiive associaion beween equaliy and mobiliy. Tha is, whenever here is high mobiliy, here is low inequaliy. There can, of course, also be a siuaion in which here is no mobiliy a all. In such a siuaion, a handful of skilled workers have high wages ha enable hem o educae all of heir children while wages for unskilled workers are so low ha educaion is no affordable, even for he mos indusrious families. In fac, when he cos of educaion is high enough, his is he only kind of seady sae here is. 11 When he cos of educaion is below a cerain ceiling, here is a leas one high-income, high-mobiliy equilibrium. In such a siuaion, he workforce is highly educaed, which lowers he equilibrium skill wage premium and hence he chances ha an unskilled worker will find herself limied by her borrowing consrain. This no only reduces inequaliy; i also makes i easier for a high-abiliy child of an unskilled worker o receive an educaion and lowers he incenive for a low-abiliy child of a skilled worker o acquire skills. In oher words, i raises boh upward and downward mobiliy. In addiion, in hese equilibria he allocaion of educaion is more sensiive o acual abiliy and less so o parenal background han i is in a more unequal economy where borrowing consrains are disproporionaely greaer for he children of low-income parens. This is, in fac, why income is higher, as he mos indusrious workers are in high-produciviy posiions. In low-income socieies, hese conclusions are reversed: he sock of skills is small, he wage differenial is high (so is inequaliy), and mobiliy is very low. As a consequence, he allocaion of resources is more inefficien. 12 Thus, credi marke imperfecions make curren skill levels dependen on pas skill levels, as embodied in parenal income. The inefficien seady saes arise from he fac ha his dependence is no based on a produciviy difference (as would be he case if, for insance, abiliy were inheriable). The key aspec of his model is ha hese differen seady saes coexis as possible oucomes for he same economy. In oher words, wo economies wih he same parameers (access o he same echnology, equal weigh given o children in he uiliy funcion) may end up wih widely differen mobiliy and inequaliy levels. If i were possible o change he siuaion in one period by means of a single (large-scale) policy 11 There can also be a coninuum of his sor of immobile seady sae. Saring from any one of hese saes, we can slighly increase he proporion of educaed individuals and reduce he wage differenial accordingly, and we will have anoher seady sae wih no mobiliy. 12 Noe ha upward and downward mobiliy move ogeher when going from one seady sae o anoher. This is because we are changing he naure of he equilibrium, and high-mobiliy equilibria are more efficien in ha hey are more sensiive o he acual abiliy of each individual. 14

17 inervenion, i would become self-susainable. In conras, he inervenions required in economies where i is a quesion of changing he fundamenals, such as Becker and Tomes, are generally long-erm policy measures. Wha would a one-ime inervenion involve? One possibiliy would be a large-scale redisribuion of income ha could be accomplished eiher by giving funds direcly o parens, by giving hem vouchers for educaion, or by using income ax revenues o subsidize public educaion anyhing ha would emporarily break he dependence of educaion on background, hereby increasing he supply of educaed workers and moving he sysem oward a low-inequaliy, high-income seady sae. Oher policy recommendaions come from ouside he model. The focus on human capial acquisiion allows Owen and Weil o consider differen policy experimens, all of hem relaed o changes in he educaion sysem. Given ha inefficiencies resul from he presence of liquidiy consrains, a (permanen) program of educaion loans is he firs opion considered. These auhors find ha such a program reduces inequaliy and raises average income, effecively moving he economy o a high-educaion, low-inequaliy seady sae. The second policy hey analyze is a meriocraic public educaion sysem, where high-abiliy individuals ge he educaion ha maximizes ne oupu. Again, his kind of policy effecively does away wih he inefficiencies creaed by he borrowing consrain. Wheher his kind of policy is maerially feasible in low-income, low-mobiliy counries depends on funcional forms adoped in he model. 13 Why would he implemenaion of a meriocraic schooling sysem be an effecive policy? The answer is ha such a sysem would end o wipe ou he differences in schooling ha arise solely by virue of parenal income: in oher words, for he same reason ha we argued ha an increase in schooling qualiy would reduce h and herefore increase mobiliy. Noe ha his is no an absrac consideraion. Counries such as China, Souh Korea and Japan have a srong public educaion secor which uses esing and assessmens early on as a basis for assigning sudens o schools and channeling hem ino careers based on heir cogniive abiliy. To a lesser exen, European counries such as Germany and France have a srong, high-qualiy public educaion secor as well. These counries also have greaer social mobiliy han Lain America. Policy Massive Redisribuion Educaion Loans Meriocraic Public Schooling Table 5: Types of Policy Inervenion in Owen and Weil s Model Type of Effec wihin he Model Inervenion One-Time Permanen Permanen Keeping fundamenals such as educaion cos he same, movemen oward a beer seady sae. Change in fundamenals: slackens liquidiy consrain. Can poenially improve upon he bes pre-inervenion seady sae. Maximizes ne oupu, breaking he link beween parenal income and educaion. 13 I is even more doubful wheher i would be poliically feasible, since in a poor counry such a measure migh enail seizing he enire labor income of an adul generaion in order o finance educaion for he young. 15

18 So far, he effecs of differences in background are unambiguously inefficien. However, his changes when skilled parens ransmi advanages because hey are, in some sense, more efficien han heir unskilled counerpars. Hassler, Rodriguez Mora and Zeira: The Roles of Educaion and Technology Moving on, Hassler, Rodriguez Mora and Zeira (2003) presen a similar seup in which workers may be skilled or unskilled and mus finance heir educaion wihou access o a loan marke. In heir seing, however, differen agens face differen coss of educaion. In order o become skilled, a child needs a cerain amoun of schooling ime, and his is affeced by wo facors: innae abiliy (which is independen across generaions and reduces he ime needed), and parenal background. High-abiliy individuals need o spend less ime obaining formal schooling in order o acquire skills, and he same is rue for children of skilled parens, who need less ouside help in order o achieve he same goals, presumably because hey have a beer undersanding of wha needs o be done and how bes o do i. This is an addiional, and plausible, pahway hrough which parenal background affecs children s well-being. There are wo alernaive echnologies in his economy: a consan-reurns-o-scale producion secor, where each skilled worker produces oupu according o her produciviy, and a secor which uses unskilled workers and naural resources as inpus (wih such resources being assumed o be equally divided among unskilled workers). The difference beween skilled and unskilled workers lies in heir produciviy, a, which can ake wo values, as an, according o he skill level. y y s n a s a x n (11) In an equilibrium, skilled workers will earn X an a s, while unskilled workers will earn anx, where X is he aggregae sock of naural resources and N he aggregae N supply of unskilled labor. The income of unskilled workers decreases when he aggregae 0,1 ). supply of unskilled workers rises (since Teachers are hired o provide his schooling ime (i.e., o produce educaion ) and are paid he skilled-wage rae. Each skilled worker who is employed as a eacher produces a cerain amoun of unis of educaion: h 1. This links innae abiliy and parenal background o educaion coss: he less ouside ime needed for he acquisiion of skills, he lower he cos of skill acquisiion. The economy consiss of overlapping generaions of individuals whose lives can be divided ino wo periods. In he firs, hey acquire skills. In he second, hey work, 16

19 consume, and inves in educaion for heir children. They derive uiliy from heir own consumpion and from he well-being of heir offspring: 14 V ln c E V (12) par par off where E is he expecaions operaor, and V is generaional uiliy. The process used o model educaion sars ou by specifying innae abiliy. This is indicaed by he amoun of ime ha a person would need o be educaed in order o become skilled, if born o a skilled paren. I is labeled inapiude and denoed by e (and is assumed o be uniformly disribued beween 0 and 1). The educaional barrier faced by children of unskilled parens is inroduced by saying ha an individual wih inapiude e needs be unis of educaion in order o become skilled if born o an unskilled household, wih b 1. Noe ha when background is inroduced in his way, is effec is no inefficien, since i acually requires more resources o educae children from poor families. This differs from he effec of liquidiy consrains, which are also presen in he model and which limi educaional invesmen even if i would be efficien o inves in an individual s educaion, given her innae abiliy. This model has a unique seady sae whose equilibrium we will now examine. Under his model, parens will choose o inves in heir children s educaion if: ln y i V ln y V where i s e / h y s be / h y s n if paren is skilled if paren is unskilled (13) Because of he srucure of preferences, boh kinds of parens will choose o spend a maximum fracion of heir income in educaion, which we will call m 15. This fracion is chosen opimally, given he value of educaion (i.e., he difference in expeced welfare beween skilled and unskilled individuals). In urn, m defines wo hreshold inapiude levels, such ha parens will only inves in educaion for lower values of e. These hresholds saisfy: es y s my s e s hm h ben y hm hm y my e h y b Ib n s n n s (14) 14 I should be noed ha hey do no care abou he amoun of resources spen on heir children in and of iself, bu raher abou he resul of heir expendiure. 15 M is obained as he soluion o ln 1 m V s Vn. 17

20 Where I is he measure of income inequaliy chosen by he auhors, given by he raio beween he incomes of skilled and unskilled workers: I y y s (15) n Noe ha, given he disribuional assumpions of e, hese hresholds give he probabiliy ha he son of a skilled (or unskilled) worker will be skilled and hus serve as indicaors of mobiliy. As expeced, he probabiliy ha he child of an unskilled worker will become skilled is lower han i is for he son of a skilled worker. Now, we wan o solve for he gains o educaion as a funcion of he fracion of income ha is spen in equilibrium in order o solve for he opimal m, given he oucomes in he labor marke: 1 Vs Vn ln I h1 ln 1 m m bi (16) Wha does equaion (16) ell us? The gains from educaion are increasing in inequaliy. This effec is propagaed hrough a direc channel in he form of wha could be ermed an income effec, bu i is also generaed by he fac ha i increases he likelihood ha children from skilled backgrounds will be more able o afford an educaion han children from unskilled backgrounds. This amplifies he advanage of being born o a skilled paren. We can also see ha gains from educaion rise when he share of income ha is alloed o educaion increases. In order o close he model, we need o know he share of individuals who will be unskilled in equilibrium, which will in urn deermine relaive wages. In oher words, we need o ake ino accoun wha happens in he labor marke. For every raio of skilled o unskilled labor supply, here is a corresponding inequaliy level, which in urn influences he proporion of income ha goes ino educaion. In a seady sae, his raio will be such ha he opimal educaion demands generaed will keep he proporions of skilled and unskilled unchanged in he following generaion. Since he model defines a unique seady-sae equilibrium, comparaive saics come from changes in he model parameers. The key finding is ha here is no unique correlaion beween inequaliy and upward mobiliy (measured by he probabiliy ha an individual born o an unskilled family will become skilled, e n ). As we have previously shown, his hm I level is given by en, where we have incorporaed he fac ha he share of Ib income going ino educaion is endogenous. There are wo effecs. Through MI, inequaliy ends o raise mobiliy by increasing individuals incenives for invesmen in educaion. However, here is also a negaive 18

21 effec, which is creaed by he difficuly of paying for a eacher when he wage differenial is high. This is he disance effec. A low levels of inequaliy, he incenive effec dominaes. When inequaliy is high, he disance effec prevails. Table 6: Effecs of an Increase in Inequaliy When Iniial Inequaliy is Low High Higher Inequaliy Increases Mobiliy Reduces Mobiliy Of course, inequaliy is endogenous and depends on he labor marke s srucural condiions. Hence, Hassler, Rodriguez Mora and Zeira firs analyze exogenous changes in he producion secor. Skill-biased echnical change raises he wage differenial for any given workforce skill composiion. This kind of change increases he incenive o acquire educaion, hereby raising he proporion of income ha goes ino educaion. I also increases inequaliy, and his laer effec acquires greaer weigh when inequaliy is already high. In oher words, skill-biased echnical change increases inequaliy he mos in economies which were already unequal. The change in mobiliy mirrors wha we said above: for low levels of iniial inequaliy, skill-biased echnical change increases upward mobiliy; for high levels of inequaliy, i reduces mobiliy. The second se of exogenous changes ha hese auhors analyze relaes o he educaional secor, ha is, changes in h and b. An increase in h, i.e., in he overall produciviy of educaion, has wo general equilibrium effecs: i increases upward mobiliy, and i reduces inequaliy. A reducion in he educaional barrier faced by children from unskilled backgrounds, as measured by b, has a less clear effec. By making invesmen by unskilled parens more producive, i reduces he fracion of income invesed in educaion across he board. This implies greaer downward mobiliy, as children from high-skill backgrounds become more likely o forgo an educaion. However, i can sill be shown ha inequaliy goes down as mobiliy goes up. Table 7: Effecs of Policies in he Hassler, Rodriguez Mora and Zeira Model Policy/Change Increase in a s Reducion in h Reducion in b Public educaion p Descripion Skilled-biased echnical change Increase in produciviy of educaional sysem Reducion in educaional barrier faced by children of unskilled parens Sae financing of p unis of educaion for every child Implemened in Labor marke Educaion secor Effec on Inequaliy Mobiliy Increase Increase / Decrease Decrease Decrease Decrease (for mos parameer values) Increase Increase Increase 19

22 The las change ha is analyzed is he inroducion of public educaion, which amouns o a cerain level of educaion, p, being purchased by he governmen (financed by axes) and given o all children, wih parens being free o supplemen ha educaion wih addiional oulays. These auhors furher assume ha here is a proporional ax on income, T, and ha h equals 1. Wih hese addiions o he original model, he educaion hresholds are modified and urn ino: 1 m es p m1t en p 1 T b I (17) The main poin is ha skilled parens make more effecive use of public educaion. Carrying ou a general equilibrium analysis similar o he one used in he original model, including he relaionship beween axes and he level of public educaion, he auhors conclude ha an increase in public educaion raises upward mobiliy and, unless boh and b are oo close o 1, reduces inequaliy. Summarizing he findings in Table 7, we see ha, here again, public inervenions ha operae hrough he educaional secor end o induce a viruous cycle of reduced inequaliy and increased mobiliy. However, i is possible ha higher inequaliy will be me by higher mobiliy, paricularly when he facors driving he increases come from he labor marke and are he resul of changes in echnology. Alhough hese hree models emphasize differen aspecs of he deerminaion of income inequaliy and inergeneraional mobiliy, hey share a number of common aspecs. The main inuiion is ha he more parenal background deermines individual oucomes, he more likely i is ha high inequaliy will be associaed wih lower mobiliy. In Becker and Tomes (1979), reducing he degree of inheriabiliy lowers inequaliy and raises mobiliy, which is effecively he same as reducing he educaional barriers faced by children of unskilled parens in he Hassler, Rodríguez Mora and Zeira (HMZ) (2003) model or relaxing he ighness of he borrowing consrain in he Owen and Weil (1998) model. In conras, when we increase incenives o inves in children saring from a relaively equal seup, we may find ha inequaliy increases ogeher wih mobiliy. This is wha happens in he Becker and Tomes model, as well as in he HMZ seup, when skill-biased echnical change increases he incenive o educaion. These models boh sugges a naural consrain on how much mobiliy can be changed and poin o policies ha may affec i. If abiliy is inrinsically inheriable, as is he family endowmen in he Becker and Tomes model, hen i is a source of permanen differences beween dynasies and a brake on social mobiliy. However, his also suggess ha effors o level he playing field hrough he use of such measures as compulsory and universal public educaion, uoring, or early inervenion programs may be successful in raising income and social mobiliy. Given he evidence ha here is a grea deal of scope for early inervenions o improve cogniive abiliies, he assumpion ha abiliy is by and large independen across generaions bu ha parenal background can give children an advanage is probably he mos relevan for policy purposes. 20