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Sheffeld Economc Research Paper Seres SERP Number: 2006010 ISSN 1749-8368 Pamela Lenton* The Cost Structure of Hgher Educaton n Further Educaton Colleges n England. June 2006. * Department of Economcs Unversty of Sheffeld 9 Mappn Street Sheffeld S1 4DT Unted Kngdom www.shef.ac.uk/economcs 1

Abstract. Ths paper examnes the cost of the ncreased provson of hgher educaton courses wthn further educaton colleges n England. We beleve ths to be the frst attempt to ft a cost functon specfcally to the further educaton sector. Cost functons for a sample of 96 colleges over a two-year perod, from 2000 to 2002, are ftted usng a panel data methodology as well as stochastc fronter analyss. We compare and contrast our fndngs wth a sample of 959 US colleges. Our fndngs ndcate that most further educaton colleges are able to beneft from economes of scale. Results from both methodologes suggest the presence of product-specfc economes of scale, substantal ray economes of scale and ndcate that hgher educaton classroom-based courses, such as busness studes, as well as vocatonal courses dsplay substantal economes of scope. JEL classfcaton: C21; C23; I21 Keywords: costs; educatonal economcs; economes of scale 2

1. Introducton In the Unted Kngdom, the provson of degree-level educaton tradtonally provded by unverstes and hgher educaton colleges (HE colleges), has been supplemented by programmes at further educaton colleges (FE colleges). FE colleges, the focus of ths paper, are complex structures many of whose orgns began n provdng vocatonal courses, for example jonery and mechancal sklls. Over tme, they have added to ther portfolo of courses a wde range of academc and vocatonal qualfcatons: n the frst place access courses, whch provde students wth a second chance opton to retake examnatons faled n school 1, but n addton vocatonal and degree programmes: the Hgher Educaton Fundng Councl for England (2006) state that currently 71% of students partcpatng n access courses progress to degree programmes. FE colleges have strong lnks wth local busnesses, are able to respond to changes n local employers needs for sklls, and reach out to all soco-economc groups wthn the communty. By contrast wth tradtonal hgher educaton nsttutons where the proporton of students from low-ncome backgrounds n the UK s low (at around 14% from socoeconomc groups III, IV and V between 1980 and 2001; Greenaway & Haynes 2003) FE colleges are much more socally nclusve, wth some 29 percent of ther students comng from relatvely dsadvantaged areas (Foster 2005); the rate of educatonal progresson especally for ndvduals from lower socoeconomc groups between the ages of 16 and 18 years has been found to be greater n FE colleges than n other nsttutons (Lenton 2006). It appears therefore that FE colleges offer a major alternatve strategy for progressng towards the UK government objectve of broadenng access to post-18 educaton for dsadvantaged socoeconomc groups. Ths paper analyses, for the frst tme, the cost structure of UK further educaton colleges. The need for an analyss of the cost structure of hgher educaton provson 3

wthn FE colleges n the UK was hghlghted n a recent DfES report (Johnes et al 2005), and the present study addresses ths need by applyng the methodology used by Johnes et al to a new dataset of Englsh FE colleges. We estmate cost functons for a panel of 96 FE colleges n England over a two-year perod and compare the results from two estmaton methods, random effects modellng and stochastc fronter analyss, to explore the robustness of our fndngs. Ths analyss s then replcated for a comparson group of 959 US tertary-level nsttutons. Our data covers the two academc years 2000-01 and 2001-02. The data are constructed from several sources suppled by the UK Learnng and Sklls Councl and nclude the staff nformaton records, ndvdualsed student records and qualfcaton records. The followng secton provdes an overvew of the lterature of cost functons wthn hgher educaton. Secton 3 dscusses the data and the methodology. In secton 4 we present our results and we draw our conclusons n secton 5. 2. The estmaton of cost functons wthn hgher educaton In common wth much of the lterature on tertary educaton (Cohn et al, 1989; Dundar & Lews, 1995) we characterse the hgher educaton nsttuton as a mult-product frm. We defne three types of economes of scale: - product-specfc economes of scale (S ) S ( y) = AIC( y ) C ( y) (1) If the value (y) S y of type exst. s greater than unty, product-specfc economes of scale for output - ray economes of scale where expanson of all outputs leads to economes of scale: SR = C( y) (2) yc ( y) 4

where C ( y) = C( y) / y represents the dfference n total cost gven the dfference n output of product alone,.e. the margnal cost of producng the th output. - fnally, economes of scope, dentfy the exstence of synerges between outputs: SC [ C y,0,0) + C(0, y, y ) C( y, y, y )] C( y, y, y ) = (3) ( j k j k j k Global economes of scope exst f economes exst for producng the outputs jontly n one frm rather than separately: SG = C( y ) C( y) C( y) (4) where C(y ) s the cost of producng a gven output type n solaton and C(y) s the cost of producng all output jontly If the value for S G s greater than zero, then global economes of scope exst. Prevous estmatons of cost functons n hgher educaton (Verry and Layard (1975; Glass et al 1995) have used ordnary least-squares (OLS) analyss, whch assumes that producton s effcent. In order for such analyss to be meanngful t must be assumed that FE colleges seek to mnmze ther costs; however, n a nonproft sector, ths assumpton s questonable n the UK context, albet the sector has become much more compettve n recent years. If effcent producton cannot be assumed, then an approach such as stochastc fronter analyss (SFA) ( Johnes et al 2005), whch provdes a means of estmatng the parameters of the cost functon of a techncally neffcent producer, may be approprate, and n ths study the technque s used as a complement to OLS analyss. 3. The data and methodology The UK data used n the present study come from a sample of 96 FE colleges, for the years 2000-01 and 2001-02, wthn the Learnng and Sklls Councl s (LSC) datasets. 2 Total operatng costs, as n the vast majorty of emprcal analyses of costs n hgher educaton, are treated as the dependent varable: Table 1 shows descrptve 5

statstcs for total operatng costs, hgher educaton and further educaton outputs. Our measure of outputs, followng normal practce (e.g. Koshal & Koshal 1999) s based on full-tme equvalent (FTE) student numbers. 3 It s also mperatve to dstngush between course types: we are able to separate hgher educaton students by broad course type that groups scence subjects, classroom based subjects and vocatonal subjects. 4 Table 1 clearly shows us that some of the outputs take a value of zero, hence a quadratc model s approprate here. We estmate both lnear and quadratc models and compare the results. Estmaton of the quadratc cost functon s as follows: y = α + β x + γ x x + δ x x + ε 1 7 k 1 5 j 5, j j = 1 j j (5) where: y represents total operatng costs ( 000 per annum) x 1 through x 7 represent full-tme equvalent (FTE) student numbers n hgher educaton scences; FTE student numbers n hgher educaton vocatonal ; FTE student numbers n hgher educaton classroom; FTE student numbers n further educaton hgh ; FTE student numbers n further educaton low ; a vector reflectng teachng qualty ; a vector reflectng the qualty of the student ntake. It has been argued that any measure of the outputs of hgher educaton should reflect the qualty of teachng (Getz et al 1991), and also that the qualty of the student ntake must be consdered (Koshal & Koshal 1999). We have attempted to capture the qualty of teachng n several ways; frstly, by the estmaton of a cost functon whch ncludes the staff-to-student rato, secondly, by ncludng the proporton of teachers who hold a degree; thrdly, by ncludng a measure of the proporton of teachng staff to total staff. 5 ; and fnally, by estmatng a model whch ncludes as an nput the average pay of teachng staff at each college. 6 The measure for the qualty of the 6

student ntake s problematc because the qualfcaton-on-entry nformaton s ncomplete n the student record fles; hence we utlse the average pont score of the student ntake for each nsttuton, as recorded by the UK Department for Educaton and Sklls. 7 To control for the fact that FE colleges n dfferent geographcal areas may face separate nput prces (for example costs may be hgher n the nner London area than n the mdlands and north) we nclude dummy varables for each of the nne Englsh local government regons. 8 Our U.S. data come from the Natonal Center for Educaton Statstcs (NCES) ntegrated postsecondary educaton data system (IPEDS) for fscal years 2000 and 2001. These data provde nformaton for each nsttuton on fnance, compensaton and enrolments. Our dependent varable s the nsttuton s total recurrent expendture whch s a functon of sx outputs; research, full-tme equvalent students n graduate programs, undergraduates n professonal, scence and classroom based subjects and non-degree seekng students 9. After omttng nsttutons wth mssng varables we have a balanced sample of 959 nsttutons across our two years of nterest, whch comprse 564 prvate and 395 publc nsttutons. We also construct a subsample of colleges wth a postve number of non-degree seekng students to enable an accurate comparson between Englsh FE colleges and ther approprate US counterpart. 10 Sample statstcs for our varables of nterest are presented n Table 1. As dscussed earler, we model our cost functon by use of two technques: frstly the random effects method (Nerlove, 1971). y t = x β + ( α + u ) + ε ' t t (6) where; y t s the observaton of total cost for the th college n the tth tme perod x t s the matrx of k explanatory varables (not ncludng a constant) α s the ntercept term and denotes the mean of the unobserved heterogenety 7

2 u ~ IID(0, σ ) and s the random heterogenety specfc to the th u observaton ε t ~ IID(0, 2 σ ε ) and s uncorrelated over tme. and second, to cover the possblty that producton may not be effcent, stochastc fronter analyss, whch entals fttng the cost functon through our data ponts wth a bas toward the data ponts that ndcate a lower cost for a gven level of output. In ths technque we assume that the regresson resduals can be splt nto two statstcally ndependent components. We assume the frst component, measurement error, follows a normal dstrbuton and that the other component, desgned to capture neffcences, follows a half-normal dstrbuton (Agner et al 1977). x = f ( y 1,... y ) + ε (7) m where ε = v + u and x ndcates the nputs and y the m outputs of the th FE 2 college. ε = v + u such that v N( 0, σ ), u and v are statstcally ndependent and u 0. ~ v By usng a quadratc specfcaton of ths model, where nteractons between the outputs and squared terms are ncluded, we can determne the presence of economes of scale and scope. 4. Results Cost functons for FE colleges- lnear models We start (Table 2, columns 1 through 4) by analysng our estmates from the basc lnear functon. Our estmated coeffcents are hghly sgnfcant across both specfcatons wth the excepton of the coeffcent on hgher educaton n the scences whch we beleve s due to the extremely low number of students selectng ths opton. 11 Comparson of estmaton methods reveals remarkably smlar margnal costs for each of the FE outputs. 12 The costs attached to the provson of hgher educaton classroom-based subjects and vocatonal subjects are smlar n the random 8

effects model; however, when we drop our assumpton that all FE colleges are runnng effcently, the stochastc fronter estmates reveal that hgher educaton vocatonal courses, such as engneerng or constructon, are far less costly to provde than classroom courses 13. Our measures of teachng qualty are found to be hghly sgnfcant. The student-to-teacher rato shows a negatve relatonshp, as we would expect, wth larger classes reducng overall costs. The proporton of teachers to total staff numbers s negatve and hghly sgnfcant, mplyng that some colleges may gan effcency benefts from reducng ther rato of managers and admnstrators to teachng staff. The proporton of teachers holdng a bachelor s degree s hghly sgnfcant and, as we would expect, ncreases average costs. 14 Gven our results, we feel ths ndcates the mportance of ncludng a measure of teachng qualty n the model. Teacher pay s sgnfcant when ncluded alone but reduces n sgnfcance when the other teachng qualty measures are ncluded; therefore t may not actually be measurng ths qualty dfference 15. Our measure of the qualty of the student ntake s never sgnfcant, consstent wth other fndngs n ths feld (Johnes et al 2005); the regonal dummes, except n the South-West, are all nsgnfcant. Utlsng the results from the stochastc fronter model n Table 2, effcences for each quartle are derved. 16 Accordng to ths specfcaton, at least a quarter of FE colleges are hghly effcent, wth the thrd quartle havng an effcency score of 0.90. However, wth a mean (1 st percentle) score of 0.84 (0.82), some sxteen (eghteen) percentage ponts below unty, there appears to be room for gans n cost effcency for many colleges. In order to obtan a clearer pcture of the effcency scores we explored, n table 3, the characterstcs of our most and least effcent FE college. In ths analyss, the qualty of the student ntake takes a smlar value n both FE colleges and the most effcent FE college has a greater student -teacher rato. 17 Quadratc models 9

Our results lead us to hypothesse that there are effcency gans wth respect to resource allocaton to be made by ncreasng the numbers of hgher educaton students n FE colleges. We nvestgate ths hypothess by examnng whether or not economes of scale or scope exst from expandng the proporton of students n each of our categores. In order to do ths we estmate, n table 4, models usng the quadratc specfcaton that ncludes nteracton and squared terms nvolvng student numbers of all types. The ft of the random effects model s clearly good (R-squared = 0.90). The SFA quadratc specfcaton reveals some sgnfcant nteractons between the hgher educaton subjects and further educaton hgher-level (e.g. A levels), and a test of the restrcton that the coeffcents on all the nteracton and quadratc terms are zero ndcates that the nteracton and quadratc terms are n fact jontly sgnfcant and should be ncluded n the model. 18 Ths fndng s smlar to that of Johnes et al (2005). The estmates of the quadratc model are used to calculate our economes of scale and scope. In Table 5 we present the average ncremental costs for each type of student per annum, estmated usng the coeffcents from the stochastc fronter estmates reported n table 2. 19 The fgures n the frst column reflect the costs for an nsttuton producng the mean value of all outputs. As ths s a hypothetcal nsttuton we contrast these estmates wth those taken from a FE college wth medan levels of output and shown n column 2. Both models produce remarkably smlar average ncremental costs. HE vocatonal courses are by far the most expensve to provde (at an average cost of over 17000, the estmates of the quadratc model are much hgher than the lnear specfcaton). Other types of courses are far cheaper: average ncremental costs of HE arts courses, at 5600 per student-year, are only one-thrd of the costs of vocatonal courses, followed by FE hgher and then FE lower. Comparson of FE colleges wth other UK HE nsttutons 10

Whlst we have argued that FE colleges provde a route through hgher educaton for specfc groups of ndvduals, such as those of lower socoeconomc status who otherwse would not see hgher educaton as a vable opton, we nevertheless nvestgate here the cost of ncreased provson of hgher educaton between FE and HE nsttutons. Table 6 reports a comparson of estmates of these costs, along wth scale and scope economes between FE colleges, all hgher educaton nsttutons and HE colleges 20. Here we clearly see that our estmate of the cost of classroom-based hgher educaton courses n FE colleges s remarkably smlar to the cost of provdng these courses n hgher educaton colleges and close to the cost of provdng these courses n a tradtonal unversty. In essence, there are sgnfcant economes of scale to be exploted wthn the FE college, both n vocatonal and classroom based degreelevel courses, whereas they are exhausted wthn the unversty sector. In addton, our estmates reveal that the margnal cost attached to a student takng a hgher educaton vocatonal subject wthn an FE college s some 1500, on average, less than the cost of non-scence undergraduates found n ether HE colleges or across all nsttutons. We are unable at present to dentfy and nclude a measure of the value added by further educaton colleges 21, whch means that our estmates are lkely to be based upwards. The pattern of results for ray economes of scale and global scope economes appear dentcal across all nsttuton types, revealng that economes of scale are present for all nsttutons and scope economes ubqutous. Quadratc model US colleges We now compare our results for Englsh colleges wth our samples of US tertary-level nsttutons drawn from the IPEDS database 22. The estmates for our sample and subsample of US colleges are very smlar and are presented n Table 7. The overall ft of the random effects models s clearly good (R-squared= 0.96 n both samples). Both technques reveal some sgnfcant nteractons between non-degree 11

seekers and most of the other outputs. We fnd that the compensaton pad to teachng staff has a sgnfcantly postve effect on costs and that the staff-to-student rato has the expected negatve relatonshp wth costs. A test of the restrcton that the coeffcents on all the nteracton and quadratc terms are zero ndcates that the nteracton and quadratc terms are n fact jontly sgnfcant and should be ncluded n the model. Sgnfcant dfferences exst between our Englsh and US samples. The characterstc US college s a well-establshed provder of hgher educaton, conducts research and has a large proporton of degree seekng undergraduates and/or graduate students, whereas the Englsh FE college s stll evolvng as a provder of hgher educaton and as such has a much larger share of further educaton students (nondegree seekers). 23 Economes of Scale and Scope FE colleges and US colleges We report n table 8 the economes of scale and scope for the Englsh and both US samples, derved usng both estmaton methods. Followng Laband and Lentz (2003) we examne economes of scale and scope from the expanson of all types of students at each nsttuton by calculatng all economes at both mean values and twce mean values of the outputs 24. The strkng smlarty n the predctons of scale economes from both estmaton methodologes n both countres s clearly evdent. For Englsh colleges there s evdence of large product-specfc economes of scale for hgher educaton arts courses and dseconomes of scale for scence subjects. The random effects model provdes evdence of economes of scale stll to be exploted for HE vocatonal courses; however, the stochastc fronter estmates mply that these are exhausted. Usng the estmates from both methodologes we fnd there are sgnfcant ray economes of scale. Whlst ths result s ntally puzzlng, gven the dseconomes found for scence subjects and only small economes of scale for vocatonal courses, the paradox s explaned by the fndng of economes of scope, whch are present for 12

all course types. 25 Ths ndcates substantal synerges between the course types and qualfcaton levels. Both models predct hgh economes of scope for vocatonal subjects and both predct sgnfcant global economes of scope. Ths fndng appeals to ntuton f we consder that laboratores or workshops once constructed can be used for the teachng of further educaton or hgher educaton courses. We consder that our results confrm our hypothess that the expanson of hgher educaton wthn colleges can ncrease cost-effcency. 26 There are product-specfc economes of scope to be exploted n both vocatonal and arts hgher educaton courses as well as FE courses. The large global economes of scope found from both specfcatons ndcate cost effcency gans from expandng all these types of provson smultaneously. Columns 3, 4, 6 and 8 of Table 8, reportng our economes for twce the mean value of students, reveal that whlst most economes of scale and scope have been exhausted there are stll economes of scale to be exploted for hgher educaton courses n the arts. The scale economes calculated for US colleges reveal that product-specfc economes are largely exhausted, especally n our subsample where some dseconomes are found. However, the calculatons resultng from the random effect estmates from our full sample ndcates that there are further product-specfc economes of scale to be exploted from expandng outputs of classroom-based undergraduates. The random effects model also suggests that there are productspecfc economes present for research n both our US samples. Usng both technques we fnd that substantal ray economes of scale are acheved n both samples, from ncreasng all outputs proportonally. Lookng across the table to columns 3 and 7, we can see that a doublng of all nputs would lead to ray dseconomes. However, as Laband et al (2003) pont out, unverstes do not typcally experence proportonate growth of ther outputs. The two methodologes dsagree n ther fndngs of economes of scope. Small economes of scope are found usng the 13

random effects estmates suggestng that these are nearly exhausted, hence US colleges are utlsng the synerges between ther outputs to the full. As mentoned above, the two college types we have compared are not dentcal ether n ther evoluton or ther current outputs. However, our results suggest that US colleges enjoy a cost advantage n the provson of hgher educaton courses, namely a spreadng of teachng and space resources, permttng greater effcency n resource allocaton; but by comparson wth the Englsh system, ths cost advantage has already been fully exploted, especally n our subsample, whereas the potental cost advantage of Englsh further educaton colleges s under-exploted. 5. Conclusons We have estmated cost functons for a two-year panel of 96 colleges of further educaton n England by comparson wth two panels of 959 and 719 colleges n the US. The FE college n England, beng accessble to all soco-economc groups and provdng a potental brdge to enrolment n hgher educaton programmes, s strategcally vtal to the UK government s am of unversalsng access to tertary educaton. The analogous US college system ncludes both prvate and publc nsttutons whch we analyse together. We use random effects and stochastc fronter methods to model our cost functons. Our Englsh models nclude measures of full-tme equvalent student numbers. Our measure of student qualty was found to be nsgnfcant; however, teachng qualty varables were found to be hghly sgnfcant, thus supportng the clam by Getz et al (1991) that teachng qualty at the nsttutonal level must be taken nto consderaton when comparng levels of cost effcency. Estmaton of the lnear specfcaton by stochastc fronter analyss reveals that although there s room for substantal cost effcency gans n at least half the cases examned, hgher educaton vocatonal courses are the most cost-effcent. Ths 14

supports our vew that FE colleges, lke communty colleges n the US, can provde the lnk between the hgh level of vocatonal sklls requred by the local busness communty and students who, for whatever reason, dd not make the grade the frst tme around. Thus, even though the market for hgher educaton s far from perfect (Dll 1997) there s a presumpton that competton serves as a vehcle to ncrease effcency (Hoxby 2002, Barr 2004). Polcy measures whch would make such competton easer such as, n the UK, a change n unversty admssons procedures to admt students from HE colleges nto the second and thrd levels of degree courses, as s possble for communty-college students n the US are to be welcomed for ths reason. Estmaton of the quadratc specfcaton for both countres presents us wth evdence of ray economes of scale, ndcatng that cost effcences can be ganed by proportonally ncreasng the numbers of all students. For Englsh colleges we also fnd evdence of substantal economes of scope, both product-specfc and global, whereas these are found to be exhausted for our US sample. It appears therefore that whereas most US colleges have already exploted potental scale and scope economes by effcent resource management, substantal economes of scale and scope reman unexploted wthn the Englsh FE system. An expanson of numbers wthn the Englsh FE sector would appear, therefore, lkely to yeld a dvdend n terms of effcency as well as equty. Acknowledgments The author would lke to thank Sarah Brown, Gerant Johnes, Steven McIntosh, Paul Mosley and Karl Taylor for ther helpful advce and comments. In addton the author would lke to thank the Centre of Excellence, Management School Lancaster Unversty for provdng the UK data. We are also grateful to Judth Mlls of Southern Connectcut State Unversty, Vncent Tong of Gateway Communty College, CT and Jonathan Daube of Manchester Communty College, CT for ther nvaluable assstance. Fnally, our thanks go to the edtor and two anonymous referees for ther helpful comments. References 15

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Table 1: UK and US colleges: descrptve statstcs UK Varables Obs Mean Std. Dev. Mn Max Total operatng costs 2 x 96 15309.57 8346.40 2257 51786.00 HE Scence student numbers 2 x 96 27.76 45.80 0 320.17 HE vocatonal student numbers 2 x 96 91.92 174.49 0 1563.91 HE classroom student numbers 2 x 96 152.70 203.36 0 1387.82 FE hgh qualfcaton numbers 2 x 96 357.26 319.99 0 1889.15 FE low qualfcaton numbers 2 x 96 3361.80 1827.57 293.36 9616.08 Proporton of teachers to total staff (%) 2 x 96 0.55 0.09 0.239 0.75 Proporton teachers holdng a degree (%) 2 x 96 0.59 0.16 0.154 0.89 Student-to-teacher rato 2 x 96 10.24 3.93 4.80 27.94 Average teacher pay 2 x 96 4685.18 2841.20 673 18389.00 Intake qualty average pont score 2 x 96 2.93 2.23 2 7.50 US Varables Total operatng costs $000 2 x 959 105.943 207.767 2.42 2063.27 Research $ 2 x 959 28.466 91.469 0 1527.47 Graduate student numbers (000) 2 x 959 1.155 1.813 0 13.42 HE vocatonal student numbers (000) 2 x 959 0.108 0.331 0 2.62 HE classroom student numbers (000) 2 x 959 1.678 2.432 0 20.29 HE scence student numbers (000) 2 x 959 1.667 1.809 0 18.06 Non-degree qualfcaton numbers (000) 2 x 959 0.096 0.356 0 5.79 Student-to-teacher rato 2 x 959 20.31 10.348 0.894 175.22 Average teacher pay a $ 2 x 959 54.837 105.854 0.988 1159.28 US subsample a Total operatng costs $000 2 x 719 111.136 214.770 2.42 2063.27 Research $ 2 x 719 28.936 89.886 0.10 1527.47 Graduate student numbers (000) 2 x 719 1.200 1.822 0 13.42 HE vocatonal student numbers (000) 2 x 719 0.125 0.359 0 2.62 HE classroom student numbers (000) 2 x 719 1.732 2.343 0 20.29 HE scence student numbers (000) 2 x 719 1.698 1.798 0 18.06 Non-degree qualfcaton numbers (000) 2 x 719 0.133 0.417 0.01 5.79 Student-to-teacher rato 2 x 719 12.02 7.042 03.75 175.22 Average teacher pay a $ 2 x 719 57.713 109.512 0.988 1159.28 a Subsample refers to colleges wth a postve number of non-degree seekng students. Table2: Englsh FE colleges: estmated coeffcents of the lnear specfcatons Specfcaton 1 Specfcaton 2 Total operatng costs Random Effects Stochastc Fronters Random Effects Stochastc Fronters N= 96 X 2 Coeffcent (z) Coeffcent (z) Coeffcent (z) Coeffcent (z) HE Scence -3.274-0.46 1.022 0.21-4.122-0.58 1.552 0.3 HE Vocatonal 5.346 2.41*** 3.822 2.28** 5.028 2.24** 3.218 1.93** HE Classroom 4.979 2.97*** 5.822 4.27*** 4.931 2.88*** 5.634 4.03*** FE Hgh qualfcaton 4.237 6.28*** 4.530 7.81*** 3.673 5.05*** 3.890 6.31*** FE Low qualfcaton 3.553 21.51*** 3.336 24.79** 3.394 18.63*** 3.151 20.42*** Proporton of teachers 3117.288 1.81*** 1679.936 1.2 - - - - holdng a degree Proporton of teachers -7946.118-2.62*** -7658.071-3.09*** - - - - To total staff Student/teacher rato -233.445-3.56*** -200.743-3.71*** - - - - Average teacher pay - - 0.212 1.89** 0.214 2.08** Intake qualty -226.117-1.56-150.489-1.28-214.727-1.48-161.002-1.35 Year1 (2000-01) -1518.943-5.56*** -1508.508-5.97*** -1761.645-6.15*** -1742.238-6.7*** South-West 2665.613 3.61*** 689.798 1.2 3056.870 4.15*** 1150.308 1.92** Constant 6850.862 3.01*** 5764.174 3.22*** 1740.821 2.04 441.740 0.66 * sgnfcant at 10% ** sgnfcant at 5% *** sgnfcant at 1% 18

Table 3: England: characterstcs of the most effcent and least effcent FE colleges Most effcent college Least effcent college Total operatng costs 000 s 20815 11765 HE Scence student numbers 38.5 0 HE Vocatonal student numbers 123 23 HE Classroom student numbers 188.6 49.6 FE Hgh qualfcaton numbers 522.3 330.7 FE Low qualfcaton numbers 5297.4 3159.4 Proporton of teachers holdng a degree.32.63 Student-teacher rato 10.7 8.0 Intake qualty average grade pont 3.8 3.6 Table 4: Englsh FE colleges: estmated coeffcents of the quadratc specfcaton Random effects Stochastc fronters Coeffcent (z) Coeffcent (z) HE Scence -11.965-0.44-5.553-0.25 HE Vocatonal 26.230 3.33*** 24.121 3.88*** HE Classroom 5.845 5.13* 4.484 1.28 FE Hgh qualfcaton 2.524 1.31 3.47 2.25** FE Low qualfcaton 2.650 5.07*** 2.316 6.06*** HE Scence squared -0.166-1.48 0.104 1.16 HE Vocatonal squared -0.052-1.99*** -0.032-1.34 HE Classroom squared -0.001-0.14 0.001 0.16 FE Hgh qualfcaton squared 0.000 0.11-0.001-0.04 FE Low qualfcaton squared 0.000 0.82 0.001 1.5 HE Scence*HE Vocatonal 0.222 1.88* 0.135 1.29 HE Scence*HE Classroom -0.165-2.12** -0.113-1.77* HE Scence*FE Hgh qualfcaton -0.028-0.90-0.037-1.45 HE Scence*FE Low qualfcaton 0.001-0.09 0.004 0.64 HE vocatonal*he Classroom 0.029 1.39 0.015 0.95 HE vocatonal*fe Hghqualfcaton -0.000-0.49-0.002 0.61 HE vocatonal*fe Low qualfcaton -0.002-1.45-0.003-2.29** HE classroom*fe Hgh qualfcaton -0.002-0.28-0.004-0.63 HE classroom*fe Low qualfcaton 0.001 0.50 0.001 0.99 FE hgh *FE Low qualfcaton 0.001 1.44 0.001 1.62 Proporton teachers holdng a degree 3037.386 1.6 1669.701 1.12 Year1-1671.661-5.77*** -1637.594-6.54*** SouthWest 2661.826 3.57*** 749.066 1.26 Constant 681.768 0.62 541.524 0.68 Lagrangan 27 tests for random effects ch 2 = 17.54: Overall R 2 0.985 Table 5: Englsh FE colleges: estmated average ncremental costs FE colleges b All nsttutons mean values All nsttutons medan values HE Scence - - HE Vocatonal 17180 15000 HE Arts 5610 5860 FE Hgher 3890 4440 FE Lower 2810 2740 b Calculated usng the stochastc fronter estmates 19

Table 6: UK: comparson of costs between FE colleges and hgher educaton nsttutons Costs 000s Economes of scale/scope e All HEIs HE colleges FE colleges All HEIs FE colleges Non-scence 4.713 4.809 3.218 0.86 1.09 undergraduate/vocatonal Non-scence 4.511 5.096 4.931 0.86 1.51 undergraduate/classroom Ray economes of scale 1.13 1.17 Global economes of scope 0.58 0.51 e for an accurate comparson these are calculated usng the random effects estmates Table 7: US colleges: estmated coeffcents of the quadratc specfcaton All US colleges N=959 x 2 US colleges subsample N=719 x 2 Random effects Stochastc fronters Random effects Stochastc fronters estmate (z) estmate (z) estmate (z) estmate (z) Non-degree seekers 1.107 0.12-9.869-0.82 4.568 0.42-13.006-0.85 Degree classroom 6.772 4.33*** 5.131 4.01*** 6.926 3.54*** 6.023 2.84*** Degree scence -0.033-0.02 1.607 1.77* 0.101 0.04 2.562 1.81* Degree professonal 58.408 5.41*** 10.3001 1.74* 61.416 4.53*** 16.057 2.00** Graduate 8.509 5.28*** 6.691 4.39*** 10.008 5.09*** 8.145 4.38*** Research 1.204 25.06*** 0.896 31.77*** 1.202 19.03*** 0.769 16.07*** Non-degree*degree classroom 9.127 3.83*** 5.893 2.38** 10.839 3.98*** 4.102 1.92* Non-degree*degree scence -6.560-2.38** -2.636-0.84-11.132-3.28*** -2.469-0.63 Non-degree*degree professonal -77.848-3.7*** -53.554-2.55*** -88.940-3.75*** -38.330-1.39 Non-degree*graduates -1.931-1.13 1.245 0.40-2.501-1.35 0.652 0.25 Non-degree*research 0.453 4.51*** 0.093 0.83 0.534 4.66*** 0.164 1.28 Degree classroom*scence -0.364-0.98-0.0168-0.08-0.953-1.82* 0.051 0.15 Degree classroom*professonal -1.084-0.58-0.912-1.16-1.346-0.59-1.912-1.57 Degree classroom*graduate -0.084-0.36 0.163 0.95 0.144 0.50 0.281 0.98 Degree classroom*research -0.017-2.09** 0.001 0.07-0.017-1.80* 0.011 2.14** Degree scence*professonal 0.976 0.37 0.795 0.66-2.265-0.64 1.459 0.65 Degree scence*graduate 0.478 1.45 0.216 0.77 0.511 1.18 0.141 0.39 Degree scence*research 0.015 0.82 0.023 3.24*** 0.043 1.78* 0.027 1.91* Degree professonal*graduate 5.535 3.33*** 5.456 5.23*** 5.072 2.57*** 5.256 4.02*** Degree professonal*research -0.069-1.99** -0.067-3.85*** -0.118-2.62*** -0.096-2.80*** Graduate*research 0.006 1.01 0.018 3.66*** 0.002 0.30 0.025 3.39*** Non-degree 2-0.932-0.44 2.122 0.37-1.562-0.66 2.849 0.55 Degree classroom 2 0.012 0.07-0.068-0.55-0.082-0.39-0.230-1.09 Degree scence 2 0.833 3.65*** 0.250 2.08** 1.247 4.26*** 0.160 0.99 Degree professonal 2-4.205-0.58 11.060 3.30*** 2.474 0.28 13.382 2.65*** Graduate 2-0.224-1.23-0.209-1.53-0.453-1.99** -0.359-2.16** Research 2-0.001-14.67*** -0.004-15.41*** 0.001-12.28*** -0.001-13.23*** Compensaton 0.745 33.75*** 0.694 54.22*** 0.759 27.61*** 0.636 35.26*** Staff/student rato -238.080-2.77*** -256.019-2.99*** -283.53-2.62*** -249.172-2.62*** Year1 3.754 5.630*** 2.991 3.52*** 4.800 5.74*** 2.852 2.67*** 2year college -10.367-0.640-23.141-0.99 - - - - Constant 3.669 1.36-10.271-2.48*** 1.855 0.52-11.080-1.80* Overall R 2 = 9636 Overall R 2 = 9577 Lagrangan tests for random effects ch 2 = 348.92 Ch 2 = 273.70 20

Table 8: UK and US colleges: economes of scale and scope Random effects estmates Stochastc fronters estmates Mean values Mean values x 2 Mean values Mean values x 2 scale scale scope scale scope scale scope HE Scence 0.31 0.18 0.42 0.12 0.45 0.12 0.41 0.09 HE Vocatonal 1.09 0.14 0.65 0.02 1.00 0.14 0.43 0.06 HE Arts 1.51 0.16 1.16 0.09 1.15 0.10 1.05 0.05 FE Hgher 1.29 0.13 1.07 0.03 1.09 0.10 1.02 0.05 FE Lower 1.04 0.13 1.0 0.03 1.01 0.06 0.97 0.03 Ray G Ray Global Ray Global Ray Global 1.17 0.51 1.06 0.24 1.24 0.43 1.05 0.16 All US colleges Research 1.05 0.02 0.73-0.01 1.08-0.15 1.00-0.01 Graduates 1.02 0.02 0.71-0.01 0.99-0.15 0.89-0.09 HE vocatonal 0.99 0.04 0.76 0.03 0.98-0.13 0.90-0.03 HE Scence 0.99 0.04 0.84 0.03 1.01-0.14 0.77-0.10 HE classroom 1.03 0.04 0.64 0.03 1.07-014 0.61-0.06 Non-degree 1.02 0.03 0.87 0.01 1.03-0.13 0.77-0.10 Ray G Ray Global Ray G Ray Global 1.05-0.22 0.87-0.15 1.12-1.28 0.93-0.85 US college subsample Research 1.05-0.01 0.85-0.01 1.05-0.14 0.64-0.02 Graduates 0.94 0.00 0.65-0.02 0.97-0.16 0.59-0.11 HE vocatonal 0.86 0.03 0.75-0.01 0.92-0.16 0.58-0.04 HE Scence 1.00 0.04 0.59 0.02 0.98-0.13 0.62-0.02 HE classroom 0.99 0.03 0.67 0.03 1.02-0.17 0.35-0.01 Non-degree 0.97 0.01 0.63 0.00 0.99-0.17 0.55 0.00 Ray Global Ray Global Ray Global Ray Global 1.07-0.30 0.88-0.18 1.14-1.30 0.77-0.54 1 Indvduals not completng hgh-school n the US take the General Educaton Dploma whereas n the UK they can attend an FE college ether full-or part-tme to retake ther courses. 2 Datasets nclude the staff nformaton records, the ndvdualsed student records and the college account records for the years 2000/01 to 2001/02. 3 Students are classfed as full-tme f, wthn ther course, they complete 450 guded learnng hours (glh). The hours of part-tme students are summed for each college. 4 Classroom subjects nclude arts, humantes and busness studes. Vocatonal subjects nclude constructon, engneerng and agrculture. 5 Staff recorded n the LSC data ncludes teachers, admnstrators, managers and techncal staff. 6 Staff detals are taken from LSC staff ndvdualsed records. The practce of measurng teachng qualty by pay s open to crtcsm (as dscussed n secton 4), but we have ncluded t here because teachers may be seen as more productve f they have experence n teachng across a range of courses and therefore may command a hgher salary. 7 Informaton and scores avalable at http://www.dfes.gov.uk 8 The nne Englsh regons comprse: South; South West; South East; East Angla; Greater London; East Mdlands; West Mdlands; North West; North East. 9 Whlst the US and Englsh college analyses consst of hgher educaton outputs of scence, classroom and vocatonal/professonal subjects, t s not possble to separate the US non-degree seekers, equvalent to the Englsh further educaton students, by hgh or low type studes. 10 Ideally one would wsh to create a subsample contanng prncpally 2 year colleges. However, over 95% of the 2 year colleges, n the data provded by IPEDS, have mssng nformaton n the subject felds leavng us wth only 10 complete records. We have endeavoured to control for the characterstcs of the 2 year college by the ncluson of a 2 year dummy n the full sample model, shown n columns 1 through 4 of Table 7. 11 Of our 96 FE colleges 37 report zero outputs, half of the remanng ones reportng extremely low numbers. 21

12 Dfferentatng the lnear cost functon partally wth respect to each output results n ts respectve coeffcent hence, the coeffcents are the respectve margnal costs. 13 The null hypothess of no cost neffcency present was tested usng the lkelhood rato test based on a comparson of the ML random effects and SFA model (Coell et al 1998 ch 9). The ch square statstc of 48.5 s suffcent for us to accept the stochastc fronters model. See Coell et al (1998). 14 Because of the wde range of types of courses on offer, not all teachng staff at each FE college are requred to hold a bachelor s degree. 15 Pay s determned by senorty and tenure as well as the ablty to teach. Therefore, whlst a measure of teachng qualty should be ncorporated n the modellng, we do not beleve that pay s an adequate ndcator of ths qualty. 16 Total effcency s gven by a score of unty. 17 We should pont out here that n ths study we are not concerned wth output qualty. 18 x 2 =23.41 wth 15 degrees of freedom 19 The average ncremental costs are not reported for HE scence as the small number partakng leads us to doubt the estmates, as alluded to on p14. 20 Estmates for HE colleges and all nsttutons relate to the same tme perod, Johnes et al (2005) 21 Value added, for example, from busness lnks wth employers and the local communty 22 The Integrated post-secondary educaton database contans all publc and prvate tertary-level nsttutons n the US. Informaton on enrolment, fnances, compensaton and students are recorded. 23 An nspecton of college characterstcs on the relevant webstes revealed that UK FE colleges have an average proporton of 7% students n hgher educaton whereas n Connectcut the correspondng proporton s 62%. 24 These measures are derved for a hypothetcal college producng average levels of all outputs. 25 The relatonshp between economes of scope and product-specfc aggregate scale economes are llustrated by Baumol et al (1988 p 74). By defnton: the ncremental costs of producng product T n solaton plus the ncremental cost of producng all other outputs barrng product T must equal the cost of producng all ouputs plus the cost of producng all outputs less the cost of product T and less the cost of all outputs excludng T. 26 The fndng of economes of scope for scence subjects s to be treated wth some cauton because there are a small number of students n ths category and we have assumed average outputs for our hypothetcal FE college. 27 The Breusch and Pagan Lagrange multpler test tests the null hypothess that var(u ) = 0 aganst the alternatve that var(u ) 0. It follows a ch-squared dstrbuton wth 1 degree of freedom. Rejecton of the null hypothess (f chsquared>6.63) suggests that the random effects model s sgnfcant (at the 1% sgnfcance level). 22