International Comparisons of Performance in the Provision of Public Services:

Transcription

1 Internatonal Comparsons of Performance n the Provson of Publc Servces: Outcome based measures for Educaton. Mary O Mahony and Phlp Andrew Stevens Natonal Insttute of Economc and Socal Research, London anuary 2004 Abstract Ths paper consders the measurement of performance n publc servce provson n an nternatonal context. It frst sets out the measurement ssues n general terms. The paper then apples these methods to estmate labour productvty n the educaton sector comparng the UK experence wth that n the US from the md 1990s. The results suggest reasonable labour productvty growth n UK educaton over ths tme perod and show the UK outperformng the US. The authors acknowledge fundng for ths research came from the Evdence Based Polcy Fund wth contrbutons from ONS/DfES/DoH/HM-Treasury. 1

2 1 Introducton Ths paper consders the ssue of measurng performance n the provson of publc servces. Frequently studes use volume of output measures such as number of students educated or numbers of medcal nterventons. An earler paper (O Mahony, Stevens and Stokes, 2002) set out the arguments for and aganst usng nformaton on fnal outcomes to measure the servces provded, such as ncreases n average years of lfe due to medcal nterventons or lfetme earnngs arsng from educaton. It concluded that there were strong theoretcal arguments n favour of usng outcome nformaton rather than relyng solely on outputs. Ths was based on the argument that the lack of market valuatons (prces), exacerbated by ncomplete nformaton, suggests fnal outcomes may yeld a more accurate measure of the effectveness of the servces provded. But the paper also ponted out that n practce t may be very dffcult to mplement an outcome based measure, n partcular to adequately take account of factors that affect outcomes but are extraneous to the servce provder. Examples are lfestyle changes that ncrease lfe expectancy or technologcal changes that ncrease the effectveness of partcular types of sklled labour. The purpose of ths paper s a frst attempt to mplement an outcome approach and to compare performance across countres n the provson of publc servces. The applcaton chosen s educaton, arguably the easest servce to measure n an nternatonal context. Nevertheless ths paper wll show that there are a number of practcal problems that need to be resolved. The paper s prmary concern s to derve a measure of relatve productvty performance for the entre educaton sector, to complement research carred comparng performance n servces n the prvate sector (O Mahony and deboer, 2001). Internatonal comparsons are an mportant benchmark n examnng performance and may often yeld more nsghts than comparsons across tme for a sngle country alone. The former s useful 2

3 n evaluatng the extent to whch dfferent systems of provson mpact on performance whereas the latter s most useful n examnng the mpact of wthn country changes. There s also an ssue relatng to expectatons on the magntudes of ncreases n servce provson or productvty over tme. O Mahony and DeBoer (2001) show that growth rates vary consderably across sectors, wth manufacturng showng on average more than 2% growth n output per hour worked between 1989 and 1999, whereas servces sectors such as fnancal and busness servces acheved no more than 1% n the same perod. Hence Internatonal comparsons can also ad n benchmarkng expectatons on what s achevable. The next secton brefly sets out the measurement ssues n general terms and presents a measure of performance to be appled to the educaton sector. The man body of the paper then apples ths method to the educaton sector wth a vew to estmatng labour productvty growth rates comparng the UK and the US n the second half of the 1990s. It begns by descrbng the output volume data avalable for the UK, underlyng the estmates of output growth n the UK Natonal Accounts. Ths secton also examnes nformaton from an outcome measure, test score results, that s frequently employed n evaluatng performance across producng unts. We argue that ths measure s senstve to weghts on the varous test score results and so does not as yet provde a practcal alternatve to output measures. Methods employed to measure earnngs outcomes are set out n secton four and regresson results for both countres are presented. Secton fve employs the resultng estmates on lfetme earnngs to estmate outcome based measures of aggregate educaton servces for the UK. It frst consders the use of these outcomes as weghts for varous types of educaton n dervng an aggregate measure. It then examnes methods that mght be used to ncorporate changes n the effectveness of educaton across tme. Fnally ths secton presents measures of UK labour nput and labour productvty that suggest growth 3

4 rates close to those acheved n the economy as a whole. Secton sx presents the outcome, nput and labour productvty results for the US and then compares results n the two countres. Ths shows the UK outperformng the US n all years. In contrast, relatve labour productvty growth n the total economy shows the US outperformng the UK n most years of the tme perod consdered here. Fnally secton seven concludes wth an outlne of extensons of the educaton applcaton n future research. 2 Outputs, outcomes and productvty: Measurement ssues. Ths secton sets out defntons and methods to measure output and nputs n publc servces. To start assume at tme t a partcular sector provdes n servces, Y, usng k nputs, X. Examples of the former are educaton at varous levels (prmary, secondary, unversty etc.) or types of medcal nterventons and of the latter are teachng staff (prmary and secondary teachers, teachng assstants and unversty lecturers) and school buldngs or medcal staff (doctors, nurses etc.) and medcal equpment. Let Q denote the quantty of servces produced, e.g. number of pupl hours by type or number of operatons. A measure of the growth n servce provson n an aggregate sector can be calculated as: D( t) Y t = w( t) D t Q ( ), t (1) Where the operator D(t) denotes the log rate of change, D(t)Y = ln(yt) ln(yt-1) and w are weghts on the types of servces provded. Smlarly productvty growth n sector can be calculated as: D( t) P t = D( t) Y t s( t) D( t) X k k, t k (2) 4

5 Where s are the weghts on the k nputs. In what follows we frst concentrate on measurng servce provson (1) and then go on to dscuss addtonal ssues relatng to the measurement of nput growth. In measurng output growth n prvate market servces the weghts w n equaton (1) are estmated by the share of each ndvdual servce n the total value of output produced,.e. (for smplcty omttng tme subscrpts) by: w = j p Q p Q (3) If (3) s averaged across tme perods t and t-1, and substtuted nto (1) then we have the commonly employed Tornqvst ndex of output growth. In addton changes n the qualty of servces across tme can be ncorporated by replacng Q n (3) by volume measures n effectveness unts. In practce ths s acheved by estmatng Q usng deflated values, wth qualty adjusted prces replacng actual market prces n the deflaton. If a servce s provded by the publc sector, however, market prces do not exst and therefore we lack a measure of the margnal beneft to consumers of the servce provded. In the past measures have been employed whereby the cost of producng servce s used as a weght. Suppose each servce uses only one nput unque to that servce, wth unt costs c, then these alternatve weghts are gven by: x = c j X c X (4) Extendng (4) to multple nputs for each output s straghtforward, wth the total cost terms replaced by a sum across nputs used. Weghts such as (4) have been used, for 5

6 example, n the cost weghted actvty ndex (CWAI) measure of the output of the UK health sector calculated by the Department of Health. An alternatve approach to cost weghts s to place value judgements on the relatve merts of dfferent types of servces. However these judgmental weghts are lkely to be controversal at best and open to abuse at worst. The man problem wth usng cost shares n publcly provded servces s that there s no market mechansm that ensures that the margnal cost of provdng the servce equals the margnal beneft to consumers and ths may result n sgnfcant dvergence between the two. For example a medcal nterventon may be very expensve but yeld lttle by way of ncreases n lfe expectancy or qualty of lfe. Cost weghtng gves such treatments an unjustfably hgh weght. In addton t s dffcult to ncorporate qualty adjustments n the cost share approach,.e. there s no natural equvalent to deflatng by qualty adjusted prces. There s no doubt that qualty aspects are mportant n publc servce provson, most notably n medcal care snce mprovements n medcal procedures are substantal and so t s mportant to nclude qualty adjustments. Technologcal nnovaton may lower the cost of provdng a partcular servce whle at the same tme renderng t more effectve. The use of cost share weghts would then lead to a lowerng of the mpact of ths servce on aggregate growth but n realty t should have a greater weght. Innovatons that allow for out-patent treatments for partcular alments at consderably lower costs have been qute common n health provson and often these are more effectve than the hosptal treatments they replaced (e.g. the example of treatment of depresson or cataracts- see dscussons n papers n Cutler and Berndt, 2001). These observatons underly the recent dsquet wth the CWAI measure for health. However these problems extend beyond the lack of markets snce much of the lterature suggests that, even when servces are prvately provded, the market prce may 6

7 not reflect the true beneft to consumers f there are nformaton asymmetres between provders and consumers. In health care the consumer has an nadequate bass for makng a judgement on whether medcal nterventons are worthwhle,.e. for makng nformed choces among both provders and types of nterventons. In addton there s an argument that health care nsurance places a wedge between the producer and consumer wth consequent moral hazard problems. Trplett (2001) argues that the most mportant dfference between servces such as health care and general market servces such as car repar s that n the latter case the consumer can sell or scrap the car but ths s not possble for the consumer of health servces (human repar). We have socal norms that prevent consumers makng ths decson. Thus even n prvate health servces, nformaton provded by the market s nadequate to allow consumers to judge the qualty of the servce they are consumng. The lack of market prces and arguments on nformaton asymmetres suggest that t may be more useful to measure performance usng outcomes rather than outputs. Lettng O denote the outcome from the provson of servce, the smplest measure s merely to sum across outputs, assumng they are measured n consstent unts as dscussed further below. The growth n ths total outcome measure s gven by: D ( t) O = D( t) O (5) The frst problem wth mplementng (5) s that outcomes are a functon of many factors other than the drect provson of a servce. For example n health care we can wrte Health outcomes (HO) as follows: HO = H (medcal nterventons, det, lfestyle, envronment, genetc factors, etc.) 7

8 Snce medcal nterventons are one of a number of contrbutng nputs to the producton of health, t s natural to measure the contrbuton of medcal nterventon by ts ncremental contrbuton. Smlarly educaton outcomes depend on a range of background varables ncludng the socal and ethnc mx of the populaton as well as the nherent ablty of the students beng educated. In general terms we can wrte servce outcomes n the form: O = Φ( Q, Z ) (6) where Z are extraneous or background nfluences. The ncremental contrbuton of the servce provded to outcomes s then gven by the partal dervatve wth respect to Q n equaton (6): Incremental contrbuton = δ (O )/ δ (Q) other nfluences constant. There are a number of methods that could be used to measure the ncremental contrbutons. At a detaled level we could focus on partcular types of servces, controllng for populaton dfferences. Thus the dsease based approach n the OECD project on Age Related Dseases (ARD) s an example whereby researchers consder detaled medcal records for a subset of the populaton (the elderly) see also papers n Cutler and Berndt, Ultmately such a detaled approach s lkely to provde the most robust fndngs but s very ntensve n research tme. Alternatvely we can use a regresson based approach by regressng outcomes such as earnngs or lfe expectancy on the servce provded and a range of control varables. Regresson methods are employed n the educaton example n 8

9 secton 3 of ths paper. Thus n prncple we can estmate a measure O*, adjustng for the nfluence of extraneous factors, and substtute ths nto equaton (5). In practce, however, t may not be possble to adjust for all background nfluences n a sngle step, n partcular f the factors that affect outcome levels are very dfferent from those that affect growth rates and nformaton on both come from dfferent data sources. In ths case an alternatve way of proceedng s to use a two step outcome flow method whereby nformaton on outcomes are frst used to calculate the weghts n equaton (1) and then the result s adjusted for outcome growth. Thus these weghts are gven by: wo = O * O * (7) where O* are outcome values havng adjusted for the nfluence of background varables. Substtutng (7) nto (1) gves the outcome flow measure as: D ( t) YOt wo( t) D( t) Q, t = (8) Although useful as a devse to weght the quantty of servces, equaton (8) does not allow outcomes to change over tme at a dfferental rate to changes n quanttes,.e. t does not take account of changes n effectveness through tme. Therefore t may be necessary to adjust equaton (8) by addng a term nvolvng some addtonal growth n outcomes. Lettng Q* denote outputs measured n effectveness unts, then deally we wsh to estmate the followng: D( t) YO' wo t D t Q t = ( ) ( ) *, t (9) 9

10 The applcaton to educaton dscusses a number of methods of ncorporatng adjustments for ncreases n effectveness, one based on an age cohort analyss and a second based on an adjustment for the mpact of educaton on long term economc growth. Nevertheless ths step remans the most dffcult to ncorporate n practce. In order to mplement (8), (9) (and n practce equaton (5)) all outcomes need to be translated nto some common metrc. Otherwse we would have to nclude addtonal weghts n defnng O* n equaton (7) and hence would be essentally back to where we started wth equaton (1). One approach would be to translate all outcomes nto monetary values, adjustng for general nflaton, and ths we see as probably the best way forward. Thus n educaton the outcome would be lfetme earnngs arsng from partcpaton n educaton and n health ths would be the values of addtonal years of lfe through medcal nterventons. Note that the absolute monetary value placed on the outcomes does not feature n equaton (7) snce the weghts are outcome shares. Rather what matters s the relatve mpact on outcomes of the servces provded. The next secton sets out an applcaton of the outcome flow approach to educaton. Before dong so however we need to consder the nput sde of the productvty equaton (2). Here there s much less dffculty snce provders of publc servces must bd for nputs n the same market as prvate frms. Hence the wages pad to nputs can be used to derve cost share weghts so that aggregate nput s derved as a Tornqvst ndex of ndvdual nputs. In the remander of ths paper we only consder labour nput and labour productvty measures. Future extensons wll also ncorporate captal nputs. 3 Educaton outputs and outcomes The remander of ths paper consders the practcal applcaton of the outcome approach to nternatonal comparsons for the educaton sector. Ths s confned to a comparson 10

11 between the UK and the US. Ths servce was chosen snce, at the outset, t appeared that the measurement ssues were more transparent than n more complex areas such as health or socal servces. The prmary quantty of output measure, numbers of pupls educated, s relatvely easy to measure wth plentful data avalable to compare across countres. An obvous canddate as an outcome measure s test score results but ts use leads to some dffcultes, as dscussed further below. There s also a clearly defned outcome measure, takng the lead from orgenson and Fraumen (1991),.e. the mpact on lfetme earnngs arsng from educaton. In measurng the latter t s possble to draw on a vast academc lterature to set out the estmaton ssues and survey data can be employed to estmate returns to educaton at each level. Nevertheless a large number of measurement problems arse even n ths relatvely smple applcaton. The purpose of ths secton s to set out clearly the ssues nvolved. 3.1 Output and Outcome Measurement. In ths analyss we wll consder three measures of the output of the educaton sector, a volume measure, and two qualty adjusted outcome measures based on test scores and earnngs, respectvely. The startng pont for each measure s a Tornqvst chan lnked ndex, of the form of equaton (1), based on the growth n pupls/students n each educatonal level between tme perods t and t-1, gven by: Q t = ω, t ln( PUP, t ) (10) where PUP s the number of pupls n educaton, s the level of educaton, ω s a weghtng factor and s the frst dfference operator. By settng a base year equal to 100, the growth rates n (10) can be used to construct an ndex of the output of the educaton 11

12 sector. Ths general framework allows us to measure the annual flow of servces of the educaton sector. In ths secton we frst consder the three measures usng UK data. Followng ths we present estmates for the US and then compare the results for the two countres Volume of output The smplest volume measure s to set ω equal to the shares of type pupls n total pupls. An alternatve frequently employed volume measure s to weght each type n total pupl/student numbers by the share of total expendture on level educaton. But as argued n secton 2, ths approach s best avoded. Pupl shares ensures that the output measures are ndependent of nput changes whch s an mportant consderaton when we consder productvty growth. In ths prelmnary analyss we confne attenton to the perod 1994 to 2001 when data exst for all measures. The quantty of output measure employed at ONS s changes n pupl hours. They have n fact assumed that the hours each pupl s taught per annum s fxed so 'pupl hours' s actually measured as the total number of pupls beng taught (fulltme equvalent). Ths gves an ndcaton of the change n the volume of educaton output. Followng ONS we dvde the UK educaton system nto seven levels, nursery, prmary, secondary, further educaton (below degree level), undergraduate, postgraduate and specal schools. Table 1 shows ndex numbers from 1994 to 2001 for these categores for the UK. The fnal two rows show shares of pupl numbers n the base year 1995 and annual average growth rates across the perod. In total pupl/student numbers ncreased by 2.4 per cent per annum wth the largest ncreases n the two hgher educaton categores. Hgher educaton represented about 11% of pupl/student numbers n 1995 by 2001 ths had rsen to 13%. 12

13 Large ncreases were also found n nursery, whch however represented only a small proporton of the total. Over ths perod pupls aged 16 plus grew faster than those up to age 15 n secondary schools. Further educaton also shows above average ncreases. Table 1 Pupl/Student Numbers, UK, Secondary Further Hgher Educaton Nursery Prmary up to age 15 age 16+ Educaton Undergrad Postgrad Specal Total SH G SH95 = share n total pupls 1995, G = annual average growth rate, Thus the greatest percent ncreases have been acheved at the hgher qualty end of the dstrbuton. A straghtforward pupl weghted ndex does not capture ths qualty dfferental Qualty adjusted output: test score outcomes. An obvous canddate to construct a qualty adjusted output measure s to ncorporate the results from test scores nto the analyss. Table 2 shows a range of test score measures at dfferent educaton levels whch n theory could be appled to the volume measures n Table 1. All measures show large ncreases over the perod wth those n prmary and GCSEs domnatng. 13

14 Table 2 Test Scores: UK educaton, selected levels KS2: 1 Level 4 or greater GCSE: percent 5 or more A*-C A-levels: 2 Percent 3 or more HE: percent 1 st and 2.1 Per cent of pupls/students Index 1995= Notes: 1. Average Englsh and Maths. Note prmary test scores not avalable before 1997 so these were assumed constant up to then; 2. As % attemptng A-levels. In prncple t should be possble to utlse the nformaton n Table 2 wth the volume measures n Table 1 to arrve at a qualty adjusted measure. n order to do so we need to mpute a weght to pupls/students who acheve the threshold level relatve to those who do not reach ths level (wth the latter normalsed to equal one). Thus for each educaton level, we compute a pupl effectveness ndex PUPE = α PUP λ + (1- α ) PUP ( 11) Where α s the percent of level pupls achevng the threshold score and λ s the effectveness rato. Summng across the levels gves a qualty adjusted alternatve to equaton (10): 14

15 QE = e t ω, t ln( PUPE, t ) (12) where ω e s the share of type effectve pupls n PUPE (averaged across perod t and t-1 as n (1)). The problem n usng test scores s that there s no bass on whch to mpute the effectveness ratos, λ. In addton t s necessary to mpute a value to educaton levels not covered by test score statstcs. The most reasonable assumpton s to use the closest equvalent category for omtted ones (prmary scores for nursery and specal schools and A-levels for further educaton). Assumng λ s the same across educaton levels, calculatons based on (3) are shown n Fgure 1 for three varants together wth the volume measure for comparson purposes. These assume pupls/students achevng the threshold values are 10%, 25% and 50%, respectvely, more effectve than pupls who do not reach ths level. Ths shows that the results are senstve to the weghts employed but all three show faster growth than a crude volume measure, varyng from hgher growth of about 0.1% p.a. to 0.5% p.a. dependng on the weghts used. In realty we would expect the effectveness measures, λ, to vary by type of educaton receved but by how much s dffcult to gauge. One possblty would be to use nformaton on relatve earnngs. However detaled estmates of the mpact on earnngs of an addtonal GCSE or A-level or comparsons of graduate earnngs by grade of degree awarded are not readly avalable. 15

16 Fgure 1 Qualty Adjusted Indexes based on Test Scores for UK Educaton volume scores (1.1) scores (1.25) scores (1.5) There are a number of addtonal problems n attemptng a calculaton of ths knd. Frst the results are senstve to the cut-off pont n each ndcator. For example usng percent of pupls aged 15 wth 1 or more GCSE and the lowest 10% effectveness weght would lower the overall growth by about 0.4% per annum snce ths ndcator grows much less rapdly than the ndcator n Table 2. Further problems arse when there s a suspcon of grade nflaton so that ncreases n the scores may not reflect any true mprovement. Ths s a concern wth both secondary and hgher educaton levels. Agan ths could be dealt wth f there were detaled data on earnngs f mproved scores are prmarly due to grade nflaton then the market wll not remunerate workers wth mproved scores. Aganst ths t may be the case that some tests are set up so that there s a general tendency for dmnshng returns to set n at some stage. Thus n prmary educaton the tests are set up so that pupls are requred to pass some (tme nvarant) threshold. Increasng effort may be requred to get pupls at the lowest end of the ablty to pass ths threshold. Fnally achevng test score results may be subject to extraneous nfluences outsde the educaton 16

17 sector, such as effort put n by parents. Ths s less mportant when consderng changes over tme than when comparng across pupls or schools at a pont n tme, but nonetheless remans a concern. 4 Earnngs outcomes. An alternatve to the use of test scores s to use nformaton from earnngs n the marketplace to weght achevements at each educaton level. Ths secton frst consders the estmaton of wage premums to educaton, controllng for other nfluences on earnngs. We then use ths nformaton to derve an earnngs outcome based approach to measure educaton provson. 4.1 Estmatng educaton wage premums and lfetme earnngs In ths study we wll concentrate on the prvate fnancal return to educaton as a measure of educaton outcomes. Whlst we do not downplay the mportance of the socal return to educaton nvestment, such research s not possble wthn the confnes of ths partcular project. The effect of educaton on labour market outcomes has a number of dmensons. Most mportant of these s the wage an ndvdual can expect to earn wth a gven level of educaton. Another factor, whch has an ndrect mpact on earnngs, s the probablty that an ndvdual wll be able to fnd a job n the frst place. There are essentally three potental labour market states an ndvdual can fnd themselves n ther lfetme: () n work; () unemployed; and () economcally-nactve. Dffcultes arse n valung the non-pecunary aspects of each of these states (non-wage benefts of workng; the value of spare tme when unemployed or nactve). orgenson and Fraumen (1991) take one extreme vew of ths when they attempt to calculate the value of each hour spent n work and lesure. They argue that ndvduals are free to choose ther hours and wll do so such that the margnal value of work and lesure are equal. The mplcaton of ths for workng 17

18 ndvduals s that each hour of lesure (except that spent sleepng) s worth the same n dollar terms as those n work. Ths has a number of dffcultes for workng people. It assumes that workers are ndeed free to choose the hours they work, or at least able to make a trade off between workng hours and wages. A dffcult assumpton to sustan s that the hgher pad have a better qualty of non-workng lfe than the less well pad. The frst step s to estmate the mpact of educaton on earnngs controllng for extraneous nfluences. In our analyss of the outcome on earnngs we wll employ a standard Mnceran human captal earnng functon 1. In the standard model estmates the log of earnngs as a functon of years of schoolng and a second or more-order polynomal of experence. For example: ln 2 ( Y ) α + α s + α e + α e + β + ε = k kc k (13) where Y = ncome, s = years of schoolng, e = experence (years n employment), C = a vector of control varables ε = s an error term ε ~ N(0,σ). There are a number of ssues relatng to the estmaton of such equatons. The frst s the queston of whether years of schoolng represent the correct measure of schoolng. Ths may be vald n countres lke the US, Card (1999) argues, but less so n countres lke Germany and France, whch have multple educaton streams. For our purpose, t s mportant to lnk expendture, va outputs to outcomes. The publc sector n general allocates funds not to an extra year of educaton, but rather to partcular types of educaton: 18

19 .e. to specfc levels (e.g. prmary), for partcular qualfcatons (e.g. the new AS level), or a partcular ntatve (e.g. targetng mathematcal sklls). Therefore, for ths study t s more approprate to replace the s term n (13) wth terms for the partcular level of educaton experenced and/or qualfcaton obtaned. That s ln 2 ( Y ) = α 0 + α1 lql + α 21e + α 22e + l k β C k k (14) where q represent l levels of educaton. In the UK the breakdown s as follows: Qualfcaton level Varable name 1. No qualfcatons NOQUAL 2. Secondary educaton up to GCSE GCSE 3. Secondary educaton up to A-Level ALEVEL 4. Trade Apprentceshps TRADAPP 5. Further Educaton qualfcaton FE 6. Hgher educaton Undergraduate HE_UG 7. Hgher educaton Postgraduate HE_PG The baselne category n the regressons s no qualfcatons. For completeness trade apprentceshps are ncluded as a separate category although these do not feature n our educaton outputs. In the US t s: 1 The study of the prvate returns to educaton has a long hstory. Davd Card provdes a useful survey of the 19

20 Qualfcaton level Varable name 1. Less than 11 th Grade th Grade GRADE th Grade, but no Dploma GRADE12N th Grade, Hgh School Dploma, GED GRADE12D 5. Some college but no degree SOMECOL 6. Assocate degree ASSDEG 7. Undergraduate degree UG 8. Postgraduate of professonal degree PG The baselne category n the regressons s educaton to less than 11th Grade. One mportant ssue to bear n mnd when consderng the effect of educaton on earnngs s the fact that we only observe wages for those ndvduals who are n work. We may not observe the wages of others for two man reasons. The frst s that ndvduals cannot fnd wage at a level that s hgh enough to entce them nto work. Because of ths, we wll not observe the lower end of the wage dstrbuton and so estmates of the effect of educaton on ncome wll be based upwards. If wages are ncreasng n educaton, ths bas wll be worse at lower levels of educaton, snce fewer ndvduals wth lower levels of educaton wll be offered a wage. Ths wll, at least n part, be offset f better educated ndvduals have hgher reservaton wages. Ted up wth ths s the fact that some ndvduals may leave the labour market for other reasons, such as chldbearng. The second reason why we do not observe an ndvdual s wage s because there s no work avalable at any wage. That s, the ndvdual s unemployed. Because of the potental for our estmates to be based, we employ a Heckman correcton/selecton methodology n estmatng wages (Heckman, 1976). In ths model equaton (14) s modfed to account for the fact that the dependent varable n the earnngs causal effect of educaton on earnngs n hs Handbook of Labor Economcs chapter (Card, 1999). 20

21 regresson s only observed f a secondary nequalty s satsfed (the selecton equaton ). That s, the dependent varable n equaton (14) for ndvdual s only observed f γz υ > 0 + (15) where the error term υ ~ N(0,1) and corr(ε, υ) = ρ. When ρ 0, a standard regresson of equaton (14) wll yeld based results. The Heckman selecton model provdes consstent, asymptotcally effcent estmates for all the parameters n such models. In the results we report the Wald test of ndependence of the selecton and earnngs equatons,.e. the lkelhood rato test that ρ = 0. In addton to reportng ρ, we also report the selectvty effect, λ = ρσ, as well as ts standard error. Before we contnue, we must note that there are two addtonal potental bases n OLS estmates of the returns to educaton. The frst s due to an omtted varable measurng the nnate ablty of an ndvdual, the second s that famly background may also affect an ndvdual s educatonal attanment. There s a long hstory of usng nstrumental varables (see Card, 1999, for a survey). These nstrumental varables analyses tend to fnd hgher returns to educaton. However, Dearden suggests that conventonal OLS estmates of the returns to educaton can generally be reled upon for polcy decsons after estmatng models whch take account of ndvdual ablty and parental nfluence on educaton. Therefore, n order to keep ths work as transparent as possble we do not follow an nstrumental varables approach. 4.2 The Influence of Educaton on Economc Actvty Another way n whch educaton has an mpact on the labour market experence of ndvduals s va ts affect on economc actvty. Not only are those wth hgher levels of educaton lkely to attract hgher wages, they are also less lkely to be unemployed and 21

22 may also be less lkely to be economcally nactve (Stevens, 2003). Therefore, when attemptng to measure the nfluence of educaton on lfetme earnngs, t s also mportant to assess the mpact on economc actvty. Therefore we estmate a multnomal-logstc model of the probablty of an ndvdual beng n one of three labour market states (employed, unemployed, nactve). The probablty that person fnds themselves n any one of these mutually exclusve states s gven by Pr = = e 3 e ( Z j) j= 1 X β j X β j (16) where X s a vector of explanatory varables, β s a vector of coeffcents to be estmated, j = 0,, 3 are the potental outcomes (0 = employment, 1 = unemployment, 2 = economcally nactve). In order to remove the ndetermnacy of the model, we normalse by settng β 0 = 0. That s, the probabltes we calculate are the probablty of the partcular outcome relatve to beng employed. The probabltes of each outcome are, therefore, Pr Pr ( Z = j) e = 1+ ( Z = 0) = for j = X β j 2 j= j= 1 e e X β j X β j for j = 1,2 (17) 4.3 The Total Effect of Educaton on Lfetme Earnngs The total effect of educaton on lfetme earnngs s the product of the wages an ndvdual mght expect to earn f workng and the probablty of not workng. Not earnng a wage nfluences our estmaton of lfetme earnngs n two ways. Frst, as we have seen, t may 22

23 bas our estmates of the determnants of earnngs f there are any systematc dfferences between ndvduals for whom we have earnngs data and those for whom we do not. Second, people wthout work wll earn nothng, or at least have a much lower level of ncome, such as unemployment beneft or nsurance. In what follows, we assume that unemployed people n the UK earn the basc rate of unemployment beneft, and those n the US earn unemployment nsurance equal to half of ther earnngs (mplctly ths nvolves two smplfyng assumptons: that they are not unemployed for perods longer than 26 weeks n a beneft year and that they do not usually earn more than the threshold). Therefore, the total effect of educaton on earnngs s E q [ ] ( emp) + UP ( unemp) + 0 P ( unemp) P ( emp) = W P 1 q q q q q (18) where E q = the total earnngs assocated wth educaton level q, W q s the predcted effect on wages from the earnngs regresson, P q (emp) s the probablty of beng employed from the actvty regresson, U s the ncome the ndvdual would obtan f they were unemployed, P q s the probablty of beng unemployed from the actvty regresson. Thus equaton (6) says that expected earnngs are the sum of the chances of beng employed multpled by the wages that would be earned, the unemployment beneft multpled by the chances of beng unemployed plus the chances of beng nactve multpled by zero (.e. we assume that ndvduals gan nothng fnancally from economc actvty) Results for the UK The results for the UK are presented n Table 4 and Table 5. These are based on data from Summer 1996 to Sprng Table 4 presents the results of the earnngs estmaton. The Wald test of ndependence s sgnfcantly dfferent from zero (χ 2 = ), clearly justfyng the Heckman selecton model. 23

24 Earnngs are ncreasng n experence and educatonal qualfcatons for both men and women, although the effect of experence s decreasng because of the non-lnearty n the specfcaton. We can see the mportance of examnng the effects of qualfcatons on wages rather than smply years of educaton by the fact than the returns to A-Levels and FE are very dfferent. Although, the coeffcents on both n our earnngs equaton are statstcally dfferent from that of on the GCSE varable, that for FE s much lower than that for A-Levels. Those wth trade apprentceshps as ther hghest qualfcaton typcally earn less than those wth FE qualfcatons. However, there has been a consderable declne n the numbers undertakng trade apprentceshps and so reflects these structural changes n the labour market. One explanaton for the dfference between the returns to further educaton and those to A-Levels s an unobserved ablty bas. It s lkely that those students who enter further educaton are have lower levels of nnate ablty, and certanly lower GCSE scores, than those who take A-Levels. In order for these estmates of returns to truly represent addtonal earnngs power engendered by further and sxth-form educaton we would need more detaled nformaton on GCSEs or some measure of nnate ablty 2. Turnng to the actvty equatons n Table 5 we see a smlar pattern emerge. The probablty of unemployment s declnng n qualfcaton level. Agan further educaton has a smaller effect n reducng the lkelhood of unemployment than A-Levels. The results are smlar for nactvty, wth the probablty of an ndvdual beng economcally nactve declnng wth educaton. Unlke the results for unemployment, those who undertake further educaton are less lkely than those wth A-Levels to be economcally nactve. 2 Although Cawley, Heckman and Vytlacl (1998) argue that measures of cogntve ablty and schoolng are so hghly correlated as to make separatng ther effects mpossble. 24

25 We can compare our results to other work by convertng our coeffcents nto a per year equvalent, to gve an estmate of the rate of return. We do ths by subtractng from the coeffcent for a partcular level that for the prevous level and dvdng ths by the years of addtonal schoolng requred for the extra qualfcaton. For example, f we wsh to consder the rate of return for a year of undergraduate study for men, we frst subtract the coeffcent for the return to an A-Level educaton from that for undergraduate studes to obtan the addtonal earnngs due to undergraduate studes ( = ). We then dvde ths number by the number of years t takes to complete undergraduate educaton (typcally three) to get a rate of return for undergraduate studes of , or 6.6%. Ths compares to the estmated average return to a year of schoolng of 6.5% n the OLS results of Chevaler and Walker (2001) for the UK n 1995 (usng the Famly Expendture Survey). Chevaler and Walker (2001) also undertake a smlar estmaton of the returns to qualfcatons usng the Brtsh Household Panel Survey (although ther breakdown of qualfcatons s dfferent). The results for postgraduate and undergraduate degrees and A-Levels are of a smlar order to ours, although ther returns to GCSEs are much hgher. Ths may be due to dfferences n specfcaton, snce ther varables have dfferent qualfcatons subsumed n them; they also nclude a number of vocatonal qualfcatons separately and do not nclude ethnc effects, but do nclude regonal effects. 25

26 Table 3 Impled Rates of Return, UK Coeffcent Years of schoolng Rate of Return Men Secondary educaton up to GCSE Same as for no qualfcatons - Secondary educaton up to A-Level GCSE Further Educaton qualfcaton GCSE Hgher educaton Undergraduate A-level Hgher educaton Postgraduate HE UG Women Secondary educaton up to GCSE Same as for no qualfcatons - Secondary educaton up to A-Level GCSE Further Educaton qualfcaton GCSE Hgher educaton Undergraduate A-level Hgher educaton Postgraduate HE UG

27 Table 4 Earnngs Equatons, UK Usng Heckman Selecton Method Men Women Earnngs equaton Selecton equaton Earnngs equaton Selecton equaton potexp *** *** ( ) ( ) potexp *** *** ( ) ( ) potexp *** *** ( ) ( ) Health *** *** *** *** problem ( ) ( ) ( ) ( ) Black *** *** *** ( ) ( ) ( ) ( ) Indan *** *** *** *** ( ) ( ) ( ) ( ) Pakstan/ ** *** *** *** Bangladesh ( ) ( ) ( ) ( ) Other Asan *** *** *** *** ( ) ( ) ( ) ( ) Mxed ** ( ) ( ) ( ) ( ) Other *** *** *** ( ) ( ) ( ) ( ) HE_PG *** *** *** *** ( ) ( ) ( ) ( ) HE_UG *** *** *** *** ( ) ( ) ( ) ( ) FE *** *** *** *** ( ) ( ) ( ) ( ) TRADEAPP *** *** *** *** ( ) ( ) ( ) ( ) *** *** *** *** ALEVEL ( ) ( ) ( ) ( ) GCSE * *** *** ( ) ( ) ( ) ( ) DKQUAL *** *** *** *** ( ) ( ) ( ) ( ) age *** ( ) ( ) age *** ( ) ( ) age *** *** ( ) ( ) marred *** *** ( ) ( ) Constant *** *** *** *** ( ) ( ) ( ) ( ) ρ σ λ (0.01) (0.01) χ p(χ 2 ) Observatons censored Standard errors n parentheses * sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1% χ 2 = Lkelhood rato test of ρ = 0 27

28 Table 5 Actvty equatons, UK Multnomal logt (omtted category = n employment) Men Women Unemp Inactvty Unemp Inactvty age ** *** ** *** ( ) ( ) ( ) ( ) age *** *** ( ) ( ) ( ) ( ) age *** *** ( ) ( ) ( ) ( ) Marred *** *** *** ( ) ( ) ( ) ( ) Health *** *** *** *** problem ( ) ( ) ( ) ( ) Black *** *** *** *** ( ) ( ) ( ) ( ) Indan *** *** *** *** ( ) ( ) ( ) ( ) Pakstan/ *** *** *** *** Bangladesh ( ) ( ) ( ) ( ) Other Asan *** *** *** *** ( ) ( ) ( ) ( ) Mxed ** * ** *** ( ) ( ) ( ) ( ) Other *** *** ** *** ( ) ( ) ( ) ( ) HE_PG *** *** *** *** ( ) ( ) ( ) ( ) HE_UG *** *** *** *** ( ) ( ) ( ) ( ) FE *** *** *** *** ( ) ( ) ( ) ( ) TRADEAPP *** *** *** *** ( ) ( ) ( ) ( ) ALEVEL *** *** *** *** ( ) ( ) ( ) ( ) GCSE *** *** *** *** ( ) ( ) ( ) ( ) DKQUAL *** * ** *** ( ) ( ) ( ) ( ) Constant *** *** ( ) ( ) ( ) ( ) Observatons Standard errors n parentheses * sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1% In order to test the senstvty of our results to the choce of year, we also performed the same analyss on data from the summer 1998 to sprng 1999 quarters. The results of these analyses are presented n the Appendx as Table 12 and Table 13. We can see that the results are farly smlar, wth returns to unversty educaton beng slghtly hgher and 28

29 those to FE slghtly lower. The fgures for the returns to A-levels and GCSEs are approxmately equal. 4.4 Results for the US The results for the US are presented n Table 7 and Table 8. Agan, the Wald test of ndependence s sgnfcantly dfferent from zero (χ 2 = ), justfyng our use of the Heckman selecton model. Earnngs n the US are also ncreasng n educaton and experence as we would expect a pror. The rate of return to the 11 th and 12 th grades (wthout achevng a dploma) are smlar, at around 8.5%. Achevng a dploma has a strong postve effect on earnngs, although t s unlkely that the comparson wth those who acheve only 10 th or 11 th grade s approprate here, snce t s lkely that most f not all of those who could acheve a Hgh School Dploma contnue untl 12 th grade and so those who drop out before 12 th grade are come from a smlar populaton to those who stay to 12 th grade and do not obtan a Dploma. Lkewse, the return to those attendng college and obtanng an assocate degree s just under 8%, whereas for those who do not obtan a degree t s actually negatve,.e. they have smlar earnngs to those who are only educated to 11 th grade. The returns to an undergraduate degree are much hgher than those to assocate degrees and there s lttle return to postgraduate degrees over and above undergraduate study. To put these fgures n perspectve, Trostel, Walker and Wooley (2002) estmate the returns to a year of schoolng n the US to be 12.99% and 14.66%, for men and women respectvely, whch s consstent wth an average of our rates of return. 29

30 Table 6 Impled Rates of Return, US Coeffcent Years of schoolng Rate of Return Men 11th Grade <11th grade th Grade, but no Dploma th grade th Grade, Hgh School Dploma, GED th grade Some college but no degree th grade Assocate degree th grade Undergraduate degree Ass deg Postgraduate of professonal degree UG Women 11th Grade <11th grade th Grade, but no Dploma th grade th Grade, Hgh School Dploma, GED th grade Some college but no degree th grade Assocate degree th grade Undergraduate degree Ass deg Postgraduate of professonal degree UG

31 Table 7 Earnngs Equatons, US Usng Heckman Selecton Method Men Women Earnngs equaton Selecton equaton Earnngs equaton Selecton equaton potexp *** *** ( ) ( ) potexp *** *** ( ) ( ) potexp *** *** ( ) ( ) Black *** *** *** *** ( ) ( ) ( ) ( ) Amercan *** *** *** Indan ( ) ( ) ( ) ( ) Asan *** *** *** *** ( ) ( ) ( ) ( ) PG *** *** *** *** ( ) ( ) ( ) ( ) UG *** *** *** *** ( ) ( ) ( ) ( ) ASSDEG *** *** *** *** ( ) ( ) ( ) ( ) SOMECOL *** *** *** ( ) ( ) ( ) ( ) GRADE12D *** *** *** *** ( ) ( ) ( ) ( ) GRADE12N *** *** *** ( ) ( ) ( ) ( ) GRADE *** *** *** *** ( ) ( ) ( ) ( ) age *** *** ( ) ( ) age *** *** ( ) ( ) age *** *** ( ) ( ) marred *** *** ( ) ( ) Constant *** *** *** *** ( ) ( ) ( ) ( ) ρ σ λ χ p(χ 2 ) Observatons censored Standard errors n parentheses * sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1% χ 2 = Lkelhood rato test of ρ = 0 31

32 Table 8 Actvty equatons, US Multnomal logt (omtted category = n employment) Men Women Unemp Inactvty Unemp Inactvty age *** *** *** ( ) ( ) ( ) ( ) age *** *** * ( ) ( ) ( ) ( ) age * *** * *** ( ) ( ) ( ) ( ) marred *** *** *** *** ( ) ( ) ( ) ( ) Black *** *** *** *** ( ) ( ) ( ) ( ) Amercan *** *** *** *** Indan ( ) ( ) ( ) ( ) Asan *** * *** ( ) ( ) ( ) ( ) PG *** *** *** *** ( ) ( ) ( ) ( ) UG *** *** *** *** ( ) ( ) ( ) ( ) ASDACA *** *** *** *** ( ) ( ) ( ) ( ) ASDVOC ** *** *** *** ( ) ( ) ( ) ( ) GRADE12D *** *** *** *** ( ) ( ) ( ) ( ) GRADE12N *** *** *** ( ) ( ) ( ) ( ) GRADE * *** *** *** ( ) ( ) ( ) ( ) Constant *** *** *** ( ) ( ) ( ) ( ) Observatons Standard errors n parentheses * sgnfcant at 10%; ** sgnfcant at 5%; *** sgnfcant at 1% 5 Lfetme earnngs and productvty: results for the UK 5.1 Lfetme earnngs as weghts: results for the UK The results of the analyss n the prevous secton gves the lfetme earnngs achevable for gven levels of educaton and gven assumptons on actvty rates. The results for the UK are summarsed n the Table 9 below. 32