Education and Family Income

Transcription

1 Prelmnary: Comments Welcome Educaton and Famly Income Jo Blanden*, Paul Gregg** and Stephen Machn* May 2002 * Department of Economcs, Unversty College London and Centre for Economc Performance, London School of Economcs ** Department of Economcs, Unversty of Brstol and Centre for Economc Performance, London School of Economcs Abstract Ths paper consders lnks between educaton and famly ncome usng Brtsh data. Complex conceptual and modellng questons underpn the educaton-ncome relatonshp and we attempt to buld up statstcal models that are suted to dealng wth these dffcultes. We begn by presentng estmated educaton-ncome relatonshps from repeated cross-secton data and then move on to consder more detaled models based on rch data from two Brtsh brth cohorts (one born n 1958, the other n 1970). All our models uncover a sgnfcant educaton-ncome correlaton. Ths emerges n models where we use changes to the UK tax system as a quasexperment to provde exogenous varatons n ncome that dfferentally benefted famles at dfferent ponts n the ncome dstrbuton. It also emerges when we control for aspects of unobserved heterogenety lnked to chldhood experences and famly background n the cohort data. Fnally, when the same models are estmated across cohorts we uncover an ncreased senstvty of educaton to famly ncome n the later cohort. Ths reveals that the prncpal benefcares of the educaton expanson were chldren from rcher famles. Therefore a key feature of the expanson n educaton seen over the perod we study was an ncrease n educatonal nequalty lnked to famly ncome. Keywords: Educaton; Famly Income; Tax Changes; Educaton Sequences. JEL Classfcaton: I2. Acknowledgements We would lke to thank Rchard Dckens for gvng us access to hs up-to-date Famly Expendture data fles and partcpants n an IFS semnar for comments. 0

2 1. Introducton Whether famly ncome s a key factor determnng educatonal attanment s a crtcal polcy queston. It matters for questons to do wth equalty of opportunty, for questons of chld welfare and for broader questons of farness n socety. Yet, despte the exstence of a large body of work on the role of ncome, we lack real nsght nto the extent to whch ncome matters, and further f ths has altered through tme. Part of the reason for ths s the emphass of the academc work on detaled measurement questons. Another part s because the queston s so closely lnked to whether government should subsdse the educaton of chldren from lower ncome backgrounds. All ths has become even more relevant today, gven sharp ncreases n ncome nequalty, and rses n educatonal attanment and partcpaton n post-compulsory educaton, seen n several countres n the last twenty years or so. In ths paper we study what has happened n the UK where ncome nequalty has rsen snce the late 1970s, and where the ncomes of households wth chldren progressvely fell relatve to households wthout chldren (Goodman, Johnson and Webb, 1997). Indeed, the poorest households wth chldren saw vrtually no rse n lvng standards for the twenty or so years snce 1979 (Gregg, Harkness and Machn, 1999). Exstng research tends to show that chldren from poorer backgrounds do less well n a number of dmensons than the rest of socety (see, for example, Gregg and Machn, 1999, 2000). However, the extent to whch ths follows from a causal relatonshp from low ncomes to adverse outturns s less clear. The fundamental queston s whether t s money tself that makes the dfference to chldren s lves and opportuntes, or whether t s actually other factors that are correlated wth ncome that drve the observed relatonshps. If ncome matters then ncreasng nequalty of famly ncomes wll translate nto nequaltes n chldren s educatonal outcomes. 1

3 However, f the key determnants of educatonal outcomes are factors lke nnate ablty, parental educaton and parentng styles then ncreased ncome nequalty should not matter for chldren s educatonal attanment. Recent US research from the US uses a varety of dfferent ways of controllng for famly background and heterogenety and generally fnds that famly ncome does have a drect postve effect on educatonal attanment. However, there s substantal varaton n both the strength of the estmated ncome effects and on when and how ncome mpacts on chldren. 1 In the UK the smple correlaton between worse educaton attanment and low ncome has been long establshed. More recently evdence has emerged that low ncome does have an ndependent effect on chldren s outcomes after controllng for key aspects of famly background and chld ablty (see Gregg and Machn, 2000, and Hobcraft, 1998). However, to be confdent that the effect of ncome has been accurately solated requres more than controllng for famly background. Unobserved chld or famly heterogenety may well reman and, f correlated wth ncome, can generate a bas n the educaton-ncome relatonshp. The task of separatng the nfluence of ncome from famly background s therefore not straghtforward. In ths paper we adopt two dfferent emprcal strateges to try and crcumvent these problems. Frst we look at the relatonshp between educaton and famly ncome n repeated crosssecton data from the Famly Expendture Survey between 1979 and 2000, a perod of rsng ncome nequalty, and also one where varous government tax changes altered famly ncome levels. We use these tax changes as nstruments for famly ncome n our chld educaton regressons. Our second approach looks n more detal at changes n the educaton-ncome relatonshp through tme usng data from two Brtsh brth cohorts, the 1958 Natonal Chld Development Study (NCDS) and the 1970 Brtsh 2

4 Cohort Study (BCS). In these data sources, born twelve years apart, we are able to follow cohort members over tme and can pay more attenton to the sequence of educaton, thereby allowng for dfferental ncome effects at dfferent levels of educatonal attanment. These surveys contan detaled chldhood nformaton that permt us to estmate educaton-ncome relatonshps that better purge the problems of unobserved heterogenety as compared to other data sources that do not contan such rch nformaton. 2 Moreover, we can use these to say somethng about the extent to whch educaton-ncome correlatons may have altered through tme. 3 The remander of the paper s organsed as follows. Secton 2 presents some descrptve statstcs on what has happened to educatonal attanment and to famly ncome n the UK over tme. Secton 3 takes some tme to dscuss ssues to do wth dentfcaton of the mpact of famly ncome on chldren s educaton. In Secton 4 we present our fndngs based on the analyss of FES repeated cross-secton data. Secton 5 then consders comparablty of estmated educaton-ncome lnks from the cohort data vs-à-vs the FES and presents cross-cohort comparsons of basc educatonncome models. Secton 6 then presents fndngs from the sequental educaton models. Secton 7 concludes. 2. Descrptve Materal In ths secton of the paper we descrbe the key patterns of change n our two man varables of nterest, educatonal attanment and famly ncome, wth partcular reference to how the changes relate to our questons of nterest. 1 See, amongst others, Mayer (1997), Duncan and Chase-Lansdale (2000), Levy and Duncan (2001), Cameron and Heckman (1998, 2001) and Acemoglu and Pschke (2001). 2 A smlar argument s made n Dearden, Ferr and Meghr (2002) who use the NCDS data to look at lnks between wages and school qualty. Ther modellng ncludes a detaled set of controls whch they argue means ther estmated models are rather lke those used from applyng matchng technques (as n Rosenbaum and Rubn, 1983). 3

5 Changes n Educaton Fgure 1 shows the rapd expanson of educaton partcpaton seen n Brtan n recent years. The Fgure shows the DfES hgher educaton age partcpaton ndex snce 1960 and shows the proporton stayng on after the compulsory school leavng age from Famly Expendture Survey data snce the late 1970s. Educaton partcpaton was at low levels at the start of the 1960s wth around 6 percent of the 18 to 19 year old age cohort partcpatng n hgher educaton. Ths rose to around 14 percent by the md 1970s, before droppng back a lttle n the late 1970s. Most of the 1980s saw small ncreases n hgher educaton partcpaton but the expanson from the late 1980s thereafter was very rapd ndeed. By the year 2000 partcpaton reached one n three. The tmng of the rapd ncrease seems n lne wth the reform of the age 16 examnatons system that took place n 1988 wth the ntroducton of the General Certfcate of Secondary Educaton (GCSE). In that year the GCSE became the publc examnaton taken by pupls at age 16+, and t represented somethng of a departure from the prevous O level system (see Gpps and Stobart, 1997). Snce ntroducton a hgher proporton of the age group takes GCSE s than was the case wth the prevous 16+ exams and there s (an often substantal) coursework assessment. Moreover the ams of the exam moved away from separatng chldren nto hgh and low educaton streams, so as to move away from norm-referenced exams where relatve performance most matters. In the GCSE system t was argued that the use of crteron-referenced assessment could get everyone (at least n theory) achevng the top grade. That the examnaton system change stmulated a rse n educaton partcpaton seems to be confrmed by the very sharp rse n stayng on rates that 3 To date not much research has used the brth cohorts to draw cross-tme comparsons. An excepton s the study of how ntergeneratonal moblty has altered over tme by Blanden, Gregg, Goodman and Machn (2002). 4

6 occurred from the late 1980s. Fgure 1 confrms that stayng on after the compulsory school leavng age had been a feature of the 1980s, wth a rse from 36 percent of 17/18 year olds n 1979, up to 44 percent by But after ths the pace of change accelerates as the 1990s sees a step change, wth the stayng on rate rsng to 73 percent by Changes n Income Our nterest n ths paper s how educaton s lnked to parental ncome and so t s nterestng to consder how changes n ncome for famles wth chldren over the same perod as the rapd rse n educaton partcpaton. Fgure 2 shows the gap n average log (equvalsed) real ncome between famles wth and wthout chldren. In 1968 average log real ncome was around 23 percent lower n famles wth chldren, and ths gap wdens to around 30 percent lower by The gap clearly dsplays cyclcal tendences as t narrows agan n the early 1980s before rsng to just beneath 30 percent n the early 1990s. The late 1990s sees somethng of a clmb back, especally n the n last couple of years. Ths Fgure does however not reveal the sharp rse n the dsperson of ncome amongst famles wth chldren. Fgure 3 shows a very sharp ncrease n ncome nequalty. The Fgure shows the evoluton over tme of the 10 th, 50 th and 90 th percentles of the log real ncome dstrbuton where each percentle s ndexed to 1 n As such t shows ncome growth at each of the percentles. After not much change n the 1970s the Fgure shows the by now famlar pattern of flat real ncome growth at the 10 th percentle for most of the post 1979 perod. Only rght at the end does the 10 th percentle ncome start to grow n real terms. On the other hand there s sgnfcant growth at the medan (of over 40 percent) and very substantal growth of around (of over 75 percent) at the 90 th percentle. 5

7 Ths pattern of rsng ncome nequalty makes t clear that famles at the top of the ncome dstrbuton made much greater gans over tme than those at the bottom of the dstrbuton. We are nterested n consderng whether these ncome trends are mportant for rsng educaton partcpaton. In the next secton of the paper we therefore consder how educaton and ncome may be lnked. We place partcular emphass on the (sometmes dffcult) modellng questons nherent n ths. 3. Exstng Lterature and Modellng Strategy Routes by Whch Income Impacts on Educaton There are many routes by whch chldren from low ncome famles can end up dong less well n the educaton system. These can be broadly grouped nto two groups, causal and non-causal. The non-causal relatonshps occur when factors that are correlated wth low ncome result n low levels of educaton. For example, we mght thnk that low ncome famles have characterstcs that leave chldren more prone to low educatonal achevement. Such characterstcs nclude nnate (genetc) ablty, low parental educaton and other less easly observed measures of adult heterogenety whch lead to lower home based chld development. Ths may also produce a lower emphass on educatonal achevement n parentng or a reduced ablty to translate parentng tme nto educatonal development. A further example would be a shock that leads to both low attanment and low ncome, such as famly break-up. In all these scenaros t s not low ncome n tself that causes reduced attanment. Causal effects of ncome on educatonal attanment can be drect and ndrect. Drect routes may occur through reduced nvestments n educatonal development outsde the school (.e. resources for hgh qualty chldcare, after school coachng, educatonal materals n the home, money for trps to zoos, days out, holdays etc.). Later on n the educatonal process the drect effects of low ncome are even more 6

8 obvous, as poorer parents may lack the resources to fund ther chldren through further and hgher educaton. Indrect routes nclude purchase of housng n a good neghbourhood that leads to a better peer group or access to a better school. Gbbons and Machn (2001), for example, hghlght that parents seem prepared to pay a lot more for housng located near to better achevng prmary schools. Another mechansm s that fnancal problems ncrease famly conflct and parental stress levels. Ths n turn reduces the ablty to engage n parentng whch s effectve n helpng chldren do well at school. Clearly we are nterested n the extent to whch one can uncover a causal relatonshp runnng from ncome to educaton. Isolatng the Causal Effect of Income The key problem n dentfyng ncome effects on educaton s separatng the effect of fxed characterstcs and shocks whch mpact on attanment of chldren from the effect of ncome. Below we set out an llustratve model to set out the ssues nvolved. Let Ht denote a chld s educatonal attanment at tme t. Ths wll be determned by prevous fnancal based nvestments made by the chld s parents and prevous non-fnancal nvestments made by the parents FI t, NFI t. If we thnk of the effectveness of these nvestments as φ and γ respectvely and add a serally uncorrelated error term u t we have t t H = φ FI + γ NFI + u 0 t t o t t Fnancal nvestments at any pont n tme are a functon of famly ncome FI = ϕy + v t t t 7

9 and we can thnk of non-fnancal nvestments are drven by fxed background famly characterstcs A and famly related shocks A t so that NFI t = λa + ρ A t However, t seems almost certan that famly background A nfluences ncome drectly and ths s currently not allowed for. 4 Hence f we estmated: t t H = β Y + v o t t To the extent that Cov(Y t, A ) 0 then the estmated β wll be based by the omsson of A and ths bas wll, n all probablty, be upwards. One thng we can do (and we do ths n our emprcal work below) s to ntroduce a set of famly characterstcs n an attempt to parameterse A. However, the dffculty that emerges here s that attrbutes A wll contan a mxture of observable attrbutes Z so that and they parameterse X and unobservable A = X + Z. Gregg and Machn (1999) have followed ths route A to gan nsght nto whether a wde set of famly and chld characterstcs create substantal upward bas on the coeffcent on a term measurng fnancal dstress n the famly from age 7 to 16. In effect they estmate: t t H = β Y + γx + v o t t But the omtted Z s now rolled up nto the error term so that v t = Z + εt where t ε s a whte nose error. So the concern surroundng the possblty of an upwardly based β remans (though now t s due to unobserved heterogenety). 4 Indeed t may also be that the effectveness parameters φ and γ are related to the A as well. 8

10 Prevous Lterature Dsentanglng ncome effects from unobserved famly or chld heterogenety requres some ngenuty. To our knowledge, sx broad approaches have been used n the context of educatonal attanment: () Random Assgnment Trals of Interventons In the US there have been a number of welfare to work programmes undertaken under expermental condtons and (subject to ther rather specfc nature) evdence from these s perhaps the cleanest and clearest avalable. The relevant populaton n the tral s dvded nto a treated group who partcpate n the programme and an untreated comparson group. The random allocaton should ensure that treatment s not correlated wth famly or chld characterstcs. Such trals have been common and vared snce 1996 when the Clnton admnstraton allowed states to admnster ther own welfare to work programmes. So under these programmes the treated receve an exogenously drven change n famly ncome. The man focus of these programmes s on gettng lone mothers nto employment (and off welfare caseloads) but some evaluatons have also consdered chld outcomes (although frequently only for chldren under 5). Natonal Evaluaton of Welfare-to-work Strateges (2000) provdes a summary analyss of many US programmes and Duncan and Chase-Lansdale (2000) buld on ths report. Programmes based on rasng maternal employment wthout offerng addtonal nwork fnancal support (job search counsellng or educaton based approaches) seemed to have modest effects on famly ncomes and rarely had sgnfcant effects on chld outcomes. But programmes nvolvng addtonal fnancal support saw sgnfcant advances n chld development for the treated groups relatve to the controls. However, the specfc samples nvolved, wth the focus always upon low ncome lone mothers, make t very lkely that the results are not generalsable. 9

11 () Cohort Groupng Acemoglu and Pschke (2001) use a cohort based approach and assume frst that unobserved heterogenety s constant across cohorts and second that the relatonshp between ths heterogenety and poston n the ncome dstrbuton s also constant. But cohorts do dffer n the relatve ncome applyng at each pont n the ncome dstrbuton because of the rse n nequalty experenced n the US over the tme perod studed. Therefore f we observe cohorts wth greater ncome nequalty also experencng greater educatonal nequalty they argue that ths s lkely to be due to ncome effects rather than famly heterogenety. They fnd that a 10 percent ncrease n famly ncome s assocated wth a 1.4 percent ncrease n the probablty of attendng a four-year college (undergraduate degree). () Sblng Studes In ths method unobserved famly heterogenety s assumed to be common to all chldren n the same famly. The varaton n famly ncomes experenced by the sblngs comes from the age gap between them. So older chldren wll exclusvely experence a perod of famly ncome pror to ther sblng s brth and the younger chld a perod after the older chld has reached 16. Ths approach therefore gans dentfcaton from lookng at ncome varatons wthn a famly rather than consderng dfferences across famles. Sblng studes requre a full ncome hstory for the tme perod consdered. Ths tme perod may be less than all chldhood years f a measure of educatonal development s used. The central problems for sblng studes are that sblngs wll often be close n age and experence common ncome patterns for most of ther chldhood and that only famles wth 2 or more chldren can be consdered. However, the tmng of ncome changes wll be dfferent and so sblng studes may gve nsght nto whether ncome matters more at specfc ages. Blau (1999) and Levy and Duncan (2001) are recent sblng studes usng US data from the Natonal Longtudnal Survey of Youth and Panel Study of Income Dynamcs respectvely. They fnd that parental ncome matters 10

12 most for young chldren, but that the magntudes are qute small. Blau (1999) also studes ntra-famly varatons focussng on mothers sblngs and therefore usng varaton between cousns to dentfy the effect of ncome. (v) Income Changes Mayer (1997) looks at whether transtory ncome fluctuatons have an mpact on chld educatonal outcomes. She uses famly ncome after the chld has reached adulthood to predct permanent famly ncome. The argument s that famly ncome after the chld has left home cannot n tself nfluence pror educatonal attanment. So any correlaton between post-chldhood famly ncome and attanment reflects an underlyng correlaton wth permanent ncome and background factors. Post-chldhood famly ncome s thus a benchmark for permanent ncome dfferences across famles. Once the permanent ncome benchmark s controlled for, chldhood ncome reflects only resdual devatons from ths benchmark and can be consdered uncorrelated wth fxed famly factors and hence free from bas. Hence t s the mpact of transtory famly ncome that s dentfed. Mayer looks at a range of chld outcomes and IQ type test scores. The addton of post-chldhood famly ncome reduces the estmated mpact of a 10 percent ncrease n ncome on years of schoolng from 1.86 to 1.68 (after condtonng on observed famly fxed characterstcs). Hence the condtonng here makes only a mnor dfference. However, the coeffcents on ncome n a range of other socal outcomes such as teenage motherhood and droppng out of school are reduced more substantally. The mpact of ths condtonng on the relatonshp between ncome and a range of IQ tests s somewhat nconclusve, wth some coeffcents fallng and some rsng. Hence she argues that most of the raw relatonshps between famly ncome and chld outcomes reflect background factors rather than ncome. But ths general concluson does not hold for educatonal attanment. The man concern wth the Mayer analyss s that ncome changes between the 11

13 two perods she consders actually reflect famly shocks that nfluence chld attanment. Blau (1999) therefore goes a stage further and estmates chld fxed effects models wth permanent elements of attanment (age adjusted test scores) and famly ncome. Hence he looks at estmates from regressons of changes n attanment on changes n ncome and fnds small and statstcally nsgnfcant effects of current mother's wage and famly ncome on chld test scores. He fnds larger effects for permanent ncome, but s clearly unable to estmate fxed effects models for these. He concludes by argung that polces affectng famly ncome are not lkely to have a bg mpact on chld development (unless they result n szable permanent changes n ncome). (v) Ordered Choce Models - Cameron and Heckman (1998, 2001) set out to nvestgate the mportance of current (short term) famly ncome on an ndvdual s decson to pursue two or four year college because of credt constrants. They set up a sequental model of educatonal development through adolescence as a seres of choces to pursue contnued educaton. Each decson s nfluenced by pror decsons and attanment allowng famly ncome and background factors to have dstnct nfluences at each stage. Cameron and Heckman also ntroduce observed pror ablty from IQ type test scores as a control for ablty. They conclude that famly ncome s mportant n terms of attanment by age 17 and the decson whether or not to complete hgh school, but not on the decson to attend college condtonal on attanment and hgh school completon. (v) Instrumental Varables Shea (2000) adopts an nstrumental varables approach to consder the relatonshp between fathers earnngs and chld outcomes, ncludng educaton, wth sources of earnngs varatons that he descrbes as luck (these are unon status, ndustry wage prema and measures of the mpact of job loss). Hs results are the only ones from the recent US work that suggest parental earnngs do 12

14 not nfluence chld educatonal attanment. The nstruments do, however, seem of dubous plausblty at best. In summary the US lterature, wth the excepton of Shea, consstently shows that famly ncome does nfluence a chld s educatonal attanment, but that the magntudes of the mpact vary somewhat. They are very small n the sblng studes, but much larger n the Mayer (1997) and Acemoglu and Pschke (2001) studes. On questons of tmng, some of the lterature also suggests that famly ncome matters most when chldren are younger. 4. Educaton-Income Correlatons From Repeated Cross-Secton Data Famly Expendture Survey Data Our frst approach to estmatng the connecton between chld educaton and famly ncome s based upon repeated cross-secton data from the Famly Expendture Survey (FES). The FES s an annual survey of around 6000 households per year (coverng around people). We look at net ncome measures n our emprcal work on the grounds that t s net ncome that s the approprate measure f one s thnkng about resources avalable for nvestment n chldren. Educaton was frst reported n 1978 and so our analyss forms a cohort of 17/18 year olds and lnks ther educaton to famly ncome and other characterstcs of them and ther parents. We therefore focus on the years 1979 to We have around 420 matched up 17/18 year olds and parents per year. Ths smallsh sample sze rather constrans our ablty to look at changes over tme and so we defer that to our later analyss based on the much larger samples n the brth cohort data. The educaton data n the FES s farly rudmentary and can be ascertaned from two questons on age left full-tme educaton and on whether the ndvdual concerned s stll n full-tme educaton. So for ths part of our analyss we model 13

15 whether ndvduals stay on n the educaton system after the compulsory school leavng age. Later on when we look at cohort-specfc panel data we consder dfferent stages of educaton, and ther sequental nature, n more detal. Approach For ndvdual we model the stayng on decson S as a functon of log(famly ncome), lny, and other ndvdual and parental characterstcs P as follows (ε s a random error) S = α + βln Y + δp + ε As S s a dscrete 0-1 (No-Yes) varable we can estmate ths model by probt methods. But the conceptual problem dscussed above remans, unobserved heterogenety wll bas the estmate f Cov(lnY, ε ) 0. One way to control for the unobserved heterogenety s to ntroduce a detaled set of varables to proxy for what mght thnk of as person fxed effects n an attempt to purge the bas of the estmated coeffcent on log(famly ncome). Wrtng the error term as a functon of the fxed background characterstcs A so that ε = A + ω and substtutng n the above equaton then gves S = α + βln Y + δp + A +ω To the extent that A controls for the unobserved heterogenety ths wll amelorate the bas n the β estmate. As noted above some authors have argued that cohort data, lke the data we consder below, can purge bas by ncluson of a detaled set of A controls. In fact, n a dfferent context n ther study of school qualty effects on wages, Dearden, Ferr and Meghr (2002) go as far as argung that the rch cohort data they use (one of the two cohorts we use) enables one to control for bas due to school selecton through ncluson of a detaled set of pre-school selecton controls. They nterpret ths as a matchng estmator n the sense of Rosenbaum and Rubn 14

16 (1983). We also adopt ths procedure n our analyss of educaton and ncome from the two Brtsh brth cohorts. But there s a serous worry that ths approach ether controls for too much or not enough so that the estmate of β remans based. The other alternatve route s to fnd an nstrumental varable for lny. A good nstrument for lny s a varable, say T, that s strongly correlated wth lny but that does not affect stayng on, S, other than through ts mpact on ncome. We beleve that the changes made to the UK tax system n the perod we study offer a convncng nstrument for famly ncome. The mechansm we are nterested n s what happens to educaton f parental ncome s shfted. One can argue that the changes to the tax system ntroduced n the UK offer precsely ths mechansm. Take the case of a cut n personal ncome taxes (several of whch occurred over our perod of study). Relatve to people n an earler cohort ths means that the benefcares of the tax cut have more relatvely more ncome. If ths boosts nvestments n chldren (drect or ndrect) then ths provdes scope for a postve lnk between educaton and ncome. As noted above, an nstrumental varable strategy n the context of educaton and famly ncome s contaned n Shea (2000) (though he only used a sngle crosssecton). Our approach has greater smlarty wth the use of tax changes to nstrument wages n a female labour supply equaton for the UK n Blundell, Duncan and Meghr (1998). It amounts to usng the changes n the tax system as a natural experment to generate tax nduced changes n famly ncome. We construct a measure of the ncome benefts of tax cuts (or ncome losses from tax gans) and use ths as an nstrumental varable. To do ths we draw upon a farly well establshed US lterature that looks at the mpact of tax changes on household ncome (see, amongst others, Lndsey, 1987, Feldsten, 1995, Auten and Carroll, 1999 and Saez, 1999). 15

17 The nstrument we use s the gap between the tax take from an ndvdual under the current applcable tax regme and the tax take under the ntal perod (1979) tax regme (uprated wth prces) as a proporton of current gross ncome. Ths s bascally the change n the average tax prce over tme. We formulate the change n the tax prce such that t reflects the ncome gans from tax cuts (or ncome losses from tax ncreases). The measure s defned as the gap between the tax take n a gven perod and a counterfactual tax take assumng the 1979 tax structure remaned n place. It s thus the regulatory changes n tax structure that drve the varatons n the tax prce. The changes made to the UK tax system are reported the Tables n the Appendx. It s clear that the tax changes were farly complex and affected dfferent components of famly ncome at dfferent tmes. We therefore use several tax prce varables that vary over tme n dfferent ways, relatng to ndvdual earnngs and natonal nsurance, household unearned ncome (excludng benefts) and beneft ncome. The man features of the tax changes over tme were as follows: ) Income Tax: basc tax rates were reduced at varous tmes n the perods and , whlst hgher rates where reduced only n In contrast, the tax free allowance and the basc rate allowance faled to grow n lne wth earnngs such that a greater proporton of ncome was subject to tax. Ths s known n the tax lterature as bracket creep (see Saez, 1999). Ths was most marked n 1981 and when tax thresholds were frozen n nomnal terms. Pror to 1990 Income Tax was based on as jont ncome for marred couples but after that date t was assessed only on ndvdual ncome. Ths swtch benefted two earner couples even though the extra tax-free allowance avalable to marred couples was reduced n value through the 1990s. 16

18 ) Natonal Insurance: by contrast employers tax rates (Natonal Insurance, NI) rose n the early 1980s. Unlke ncome taxes, NI s not leved on unearned ncome and has an upper lmt for earned ncome above whch earnngs are not subject to NI. Hence swtchng taxaton from Income Tax to NI s regressve. ) Benefts: The man Income Support (and ts precursor Supplementary Beneft) rates for famles wth chldren were broadly constant n real terms over ths perod. But as ncomes rose n real terms the value of these benefts lagged behnd average ncomes. In-work benefts (Famly Income Supplement, , Famly Credt and Workng Famly Tax Credt ) rose faster than Income Support rates especally around the transton ponts between regmes of 1988 and Correlatons Between Educaton and Income The frst two columns of Table 1 show probt estmates of stayng on equatons for 17/18 year olds from Famly Expendture Survey data from 1979 to Column 1 reports a specfcaton wth just year dummes and controls for the gender of the chld and the presence of one or two or more sblngs. The reported margnal effect s the mpact of a standard devaton reducton n ncome from the mean. It mples that a standard devaton reducton n ncome reduces stayng on probabltes by 9.5 percentage ponts. Column 2 ntroduces controls for decade brth/educaton cohorts for each parent and whether there s just one parent (normally a lone mother). The decade brth/educaton cohort s defned as whether the mother/father was born before 1930, , and after 1950 and then each brth decade cohort s dvded accordng to whether the mother or father stayed on n educaton after age 16. These nteractons capture both the ncreasng educaton levels of parents through tme and the rsng returns to educaton across cohorts of parents (see Blundell, Duncan and Meghr, 1998). The ntroducton of these controls reduces 17

19 the estmated relatonshp between famly ncome and stayng on rates by approxmately 40 percent wth the margnal effect of a standard devaton reducton n ncome standng at 5.3 percentage ponts Usng Tax Changes As Instruments For Income As we have already dscussed n some detal, there are concerns that these estmates reman based upward due to unobserved heterogenety across famles that s correlated wth both famly ncome and educatonal attanment of parents. In columns 3 and 4 of Table 1 we mplement the Instrumental Varables estmator. The generaton of the nstrument set s descrbed above and the detal of the changng tax parameters s lad out n the Appendx. Column 3 contans the frst stage log(famly ncome) regresson. Ths contans very sgnfcant coeffcents on the tax prce varables. An F-test strongly rejects that they are jontly nsgnfcant. They seem to be good nstruments n that they are strongly correlated wth famly ncome, the endogenous regressor n our model. The ncome models mostly show that famles wth bgger gans from the tax changes were hgher ncome famles. Ths s true of changes n taxes on earned, unearned and beneft ncome where the tax prce varables attract strongly sgnfcant postve coeffcent estmates. 5 The opposte s true of ncome gans from reforms to Natonal Insurance, snce there s an upper lmt to NI contrbutons that makes benefts from cuts n NI or losses from NI ncreases relatvely smaller at the upper end of the ncome dstrbuton. Column 4 reports the IV estmates of famly ncome on the propensty of the chld to stay on n full-tme educaton beyond the mnmum school leavng age. The estmates gven are Instrumental Varable Probt estmates (as outlned n Newey, 1987). The standard errors are corrected for beng derved from the frst stage 5 The postve coeffcents on the beneft tax prces reflect that the tax changes made here caused lower ncome groups to lose out snce they had negatve tax prce changes relatve to the tax prce change of zero for famles not recevng benefts. 18

20 equaton accordng to procedure outlned by Newey. 6 The estmated coeffcent falls somewhat, but remans strongly sgnfcant. The predcted margnal effect of a standard devaton reducton n ncome comes down to 3.7 percentage ponts. Ths s approach suggests a fall n the estmated effect of famly ncome on stayng on to around 70 percent of the Column 2 specfcaton. 5. Stayng On-Income Correlatons From Cohort Data The Brtsh Brth Cohorts The second approach we take s to look at the relatonshp between educaton and ncome usng data from two very rch Brtsh brth cohorts. These are the Natonal Chld Development Study (NCDS), a survey of all chldren born n the UK between 3 and 9 March 1958, and the Brtsh Cohort Survey (BCS), a survey of all chldren born between 5 and 11 Aprl The NCDS s a very rch data source that has been used n prevous work on the effects of famly background on chld outcomes n the UK (e.g. Gregg and Machn, 1999, 2000) and conssts of the brth populaton wth follow-up samples at ages 7, 11, 16, 23, 33 and The BCS has been used less by economsts, but s very smlar n style, wth data collected at ages 5, 10, 16, 26 and 30. As well as beng smlarly structured the questons asked n the two cohorts are frequently dentcal, although there are some dffcultes nherent n usng them n a comparatve study over tme. Where relevant we dscuss these below. The use of cohort data allows us to follow full sequence of the post-16 educaton development of cohort members n a way that s very dffcult from even rch cross-sectonal sources. In ths respect t our approach s closest to that followed by Mare (1980) or Cameron 6 We are grateful to Joe Harkness of John Hopkns Unversty for developng ths procedure n Stata. 7 The NCDS data have also been used to look at the transmsson mechansms that may underpn ntergeneratonal moblty: see Gregg and Machn (1999, 2000), Hobcraft (1998) or Kernan (1995). 19

21 and Heckman (1998) who use look at sequental models of educaton usng US cohort data. These brth cohorts allow us to attempt to control for the unobserved heterogenety by ntroducng a detaled set of varables to proxy for what one mght thnk of as chld fxed effects. These comprse a mxture of varables measurng experence durng the chldhood years and a set of parental characterstcs. We consder ablty scores based upon lteracy and mathematcs tests undertaken n both cohorts at age 11 (10 n the BCS). Ths sets the ntal condton for attanment by age 10/11 and acts as to proxy a chld fxed effect, so that the estmated equaton can be thought of as measurng the mpact of ncome at age 16 on chld human captal development after age 10. The model s thus a human captal trajectory based on observed attanment by age 10. Ths has smlartes to the value added type measures used to look at the mpact of school qualty and resourcng on educatonal attanment (for a revew of these see Vgnoles et al, 2000). As noted above, ths approach stll leaves a concern of resdual bas due to unobserved fxed famly or chld characterstcs beng correlated wth ncome. To get a handle of the sze (and drecton) of possble resdual bas we addtonally ntroduce a lagged ncome measure n the BCS equaton 8 n an attempt to purge the bas of the estmated coeffcent on log(famly ncome). Ths gves an estmatng equaton of S = α + β1 ln Y 16 + A + δp +β 2 ln Y 10 + v Summary Statstcs Table 2 outlnes key summary nformaton for these two cohorts. The percentage of each cohort achevng fve or more O levels rses between the cohorts from 19 to 37 percent. Lkewse stayng on n full-tme educaton post-16 rses from 29 to 46 percent. The percentage havng at least a bachelor s degree nearly doubles. 20

22 Over the same perod real ncomes only rose margnally but ncome nequalty had started ts substantal rse through the 1980s. Ths s revealed by the standard devaton of famly ncome rsng by more than 20 percent. Comparson Wth Famly Expendture Survey We begn our cohort analyss by comparng the fxed effects proxy route wth the Instrumental Varable approach from before. Ths s a useful exercse to see how well we appear to purge bas to the same extent usng the two dfferng approaches. To facltate ths comparson we constructed a BCS cohort from the Famly Expendture Survey by defnng a wndow for the FES data that contans the BCS age cohort (plus two years ether sde to generate a suffcent sample sze). Table 3 contans the results from ths comparatve exercse. It reports IV estmates from the FES BCS cohort and two BCS specfcatons that dffer n whether or not they nclude age 10 ncome. The frst two columns show the IV results. The frst stage equaton confrms that the nstruments reman powerful, as n the full sample. The IV probt estmated coeffcent for famly ncome on stayng on rates s slghtly (though not much) larger than for the full sample, wth a margnal effect showng a 5.3 percentage pont reducton n stayng on resultng from a standard devaton reducton n ncome (see Column 2). Column 3 of Table 3 reports the equvalent BCS result ncludng the same controls plus the chld test scores at age 10. Here the estmated coeffcent s above the IV estmate from the FES, though s of the same order of magntude. Column 4 ntroduces age 10 ncome as well to net out any addtonal resdual correlaton between permanent ncome and unobserved famly characterstcs. The resultng coeffcent and margnal are now only fractonally hgher than the IV estmate. Gven the very dfferent nature of these approaches the smlarty of these estmates s 8 Unfortunately, ncome s only measured at cohort member age 16 n the NCDS. 21

23 encouragng and n lne wth the dea that a robust relatonshp has been dentfed. The results suggest that a standard devaton reducton n ncome (approxmately 45 percent) reduces stayng on rates by around 5 to 6 percentage ponts gvng an elastcty of approxmately Cross-Cohort Comparsons As we have two broadly comparable brth cohorts we are also nterested n whether the educaton-ncome relatonshp has changed as ncome nequalty started to rse n the UK. As noted earler n a prevous paper ntergeneratonal ncome transmsson appears to have rsen between these two brth cohorts (Blanden et al, 2001). A strengthenng relatonshp between famly ncome and educatonal attanment s a plausble canddate to explan ths observed pattern. 9 Table 4 thus starts the cross-cohort comparson on the same bass as we have explored so far, namely lookng at connectons between stayng on n full-tme educaton beyond age 16 and ncome. In the next secton we explore the full sequence of educatonal development from age 16 onwards. As we do not have a prevous ncome measure n the NCDS we report estmates equvalent to Column 3 n Table 3. The results suggest a sharp ncrease n the relatonshp between ncome and stayng on across the cohorts. The estmated change n the relatonshp s strongly sgnfcant suggestng an ncreasng mpact of a standard devaton of ncome from 2.5 to 8 percentage ponts (n absolute terms). Note also that the estmated BCS relatonshp wth the addton of age 10 ncome (presented earler n column 4 of Table 3) remans substantally above the NCDS estmate wth no lagged ncome varable. The results n the Table strongly support the noton that there was a rse n the senstvty of educaton to parental ncome. Put another way, the chldren who benefted most from 9 In the Blanden et al (2001) paper we present a smple model argung that the extent of ntergeneratonal moblty can shft over tme due to changes n labour market returns to educaton and n the senstvty of educaton to parental ncome. 22

24 the educaton expanson that occurred over the perod we study were from rcher famles. 6. Sequental Models of Educaton-Income Correlatons From Cohort Data Motvaton As cohort members are observed several tmes t s possble to observe ther educatonal achevement at a number of key stages. It s clear that the movement towards the hghest level of schoolng s a progresson that s dependent on attanment durng prevous stages. For example, those who dd well n O levels are more lkely to stay on at school and those who stay on at 16 have a hgher probablty of gong on to complete hgher educaton. Therefore models that focus on the effect of famly ncome on fnal achevements may confound the nfluences of ncome on school attanments, the decson to stay on and the decson to go to unversty. In ths secton we attempt to dsentangle these effects by explorng a three stage model where ndvduals move through O level achevement, the stayng on decson and obtanng a unversty degree. In addton we recognse that all these stages are affected by what has gone before, so all the effects we estmate are allowed to vary by the prevous stage. The models estmated here have been substantally nfluenced by those of Mare (1980) and Cameron and Heckman (1998) for the US, who look at grade completon as a sequence where t s assumed that you must complete one grade to move to another. The UK educaton system s rather less lnear than the US and therefore our models allow for any combnaton of outcomes. As we observe O level achevement and the stayng on decson at age 16 and the degree outcome n the early 30s t s not mpossble for an ndvdual to fal both the frst stages and stll obtan a 23

25 degree. Obvously the probablty of ths s rather less lkely than the tradtonal route, as we shall see n the next sub-secton. Descrptve Statstcs Fgure 4 presents trees showng the probablty of each educatonal route for the two cohorts. Movng from left to rght we frst observe that roughly one ffth of the NCDS cohort attaned fve or more O levels at age 16. As we would expect the chances of stayng on are substantally nfluenced by whether ths was acheved or not. Of those who got 5 O levels over four ffths stay on at school after the compulsory leavng age whle ths s only seventeen percent for those wth less than 5 O levels. A smlar story can be shown for the probablty of obtanng a degree wth about 60 percent of those who obtaned 5 plus O levels who also stayed on at school (ths can be thought of as the sealed tran route through educaton) gong on to get a degree. There s, however, some evdence of ndvduals gettng back nto educaton as for those who acheved ether O levels wthout stayng on or who stayed on wthout O levels the probablty of gettng a degree s 15 percent. The BCS cohort shows a sharp rse n examnaton achevement wth 37 percent of ths cohort dong well at O level. Slghtly less of ths larger number stay on at school than they do n the NCDS, however. In contrast, a rather larger proporton that dd not do well at O level stay on as compared to the NCDS. Ths may demonstrate ncreased opportuntes for non A-level further educaton n the second cohort. Patterns at degree level are farly smlar across the cohorts. One change s a wdenng gap n the probablty of gettng a degree for young people who do well at O level but do not stay on compared to those who dd not acheve O levels but do stay (agan ths mght be because those who stayed on wthout O levels are lkely to be takng non-academc qualfcatons). Taken together the dagrams ndcate that the ncrease n educatonal attanment between the cohorts seems to be comng from an 24

26 ncrease n O level attanment, whch then flters through to the second and thrd stages. Estmated Sequental Models Our statstcal models are desgned to allow for dfferent ncome effects at dfferent educaton stages. We thus estmate a sequental model that corresponds to the trees gven n Fgure 4. Ths amounts to estmatng condtonal probt models at each node of the tree. We estmate these by Maxmum Lkelhood where we also allow errors to be correlated for the same ndvduals at dfferent stages. At a partcular stage s of the educaton sequence E the estmatng equaton s: s Pr[E = 1 E s-1 = 1,0 E s-2 s = 1,0] = α +β ln Y + δ P + A + ω Here, lke n Cameron and Heckman (1998), an event s - = 0 says (for j = 0, 1, 2) an ndvdual stops ther educaton at stage s-j and the event - = 1says they contnue on to the next stage. Our sequental model estmates these models followng the sequence gven n the tree Fgures (so the parameter estmates all have s subscrpts attached to them). Table 5 presents the ncome effects for the sequental model controllng for chldren s test scores and famly background as n the earler stayng on models. The top panel presents the NCDS, the mddle panel the results for the BCS and the lower panel the changes between the two. In both the NCDS and BCS the largest ncome effects are notced for stayng on when ndvduals have O levels and the second largest are for degree attanment when the cohort members have good O levels and stayed on. Ths s noteworthy as we know that ths tradtonal route s the most common way to move onto the next stage. If ncome has an mportant effect here t wll be mportant n determnng the overall lkelhood of stayng on and obtanng a degree. s s s E j E s j 25

27 When we look at the cross-cohort changes the frst thng to note s that, n every case but one, the ncome effects for the BCS are larger than those for the NCDS, reconfrmng the earler pcture of an ncrease n the nfluence of parental ncome on educaton. However n not all cases are these changes statstcally sgnfcant. The largest change occurs at the O level stage where the margnal effect of a standard devaton fall n log ncome rses (n absolute terms) by 3.5 percentage ponts (.e. from lowerng the probablty of obtanng good O levels by 0.9 n the NCDS to 4.4 ponts n the BCS). The magntude of ths change s hghlghted when we recall that less than a thrd of ths group stay on n the BCS so the margnal effect amounts to around 15 percent of the group mean as compared to about 8 percent for the NCDS. In addton a large rse occurred n the effect of ncome on the stayng on decson for those who dd not obtan O levels. The effect of ncome on ths decson s very small n the NCDS, but n the BCS a standard devaton drop n parental ncome reduces the probablty of stayng on for that group by 4.5 percentage ponts. The thrd sgnfcant ncrease n the ncome effects s for the probablty of gettng a degree for those who passed fve or more O levels but who dd not stay on. In the NCDS there s a sgnfcant negatve ncome effect here. Ths means that those wth lower ncome found t easer to come back and get a degree. We mght thnk that poorer ndvduals may have faled to stay on for fnancal reasons rather than because of a lack of ablty or motvaton and therefore more lkely to reenter later than ther better-off peers. By the BCS however any such advantage has been lost wth ths group showng a postve relatonshp between ncome and degree attanment. However t must be borne n mnd that n both cohorts ths group s a very small proporton of the populaton. 26

28 If we return to consder the descrptve statstcs (n the tree Fgures) t s notceable that n all the cases where a sgnfcant rse n the ncome effect has occurred there was a substantal rse n the mean of the outcome between the cohorts as well. The proporton of people achevng 5 or more O levels between the cohorts doubled, the proporton of those stayng on wth no O levels rose by 70 percent and the rse n the proporton obtanng degrees n the O levels but dd not stay on was rather lower, but stll evdent at about 30 percent. In summary, the sequental models reconfrm our prevous results that ncome and educatonal attanment have become more closely lnked over tme. The most marked ncrease n the relatonshp occurred for school examnaton achevement and for stayng on for those who dd not attan O levels. These are the two ponts wth the largest growth n numbers between the cohorts however and t appears that the addtonal opportuntes were not beng evenly dstrbuted through the populaton and, n fact, that the expanson of educaton occurrng over the tme perod we study actually ncreased educatonal nequalty. Smulatons The nature of the sequental model means that t s not possble for the effect of a change n ncome to be entrely captured by coeffcents and margnal effects alone. A change n ncome whch ncreases the proporton of people wth O levels wll means that the extra people gettng O levels now have a hgher probablty of stayng on at school and gong on to unversty. In ths secton we present some farly rough (back of the envelope) calculatons that take account of these feed-through effects. Our calculatons are based on the effect of a one standard devaton rse n log ncome on the lowest quntle of the famly ncome dstrbuton. For the smplest cases where ndvduals reman on the same part of the tree we estmate the predcted probablty of passng nto the next stage and add to ths the 27