The Economic Efficiency of Swedish Higher Education Institutions

Transcription

1 CESIS Electronc Workng Paper Seres Paper No. 245 The Economc Effcency of Swedsh Hgher Educaton Insttutons Zara Daghbashyan Dvson of Economcs, CESIS, KTH March 2011 The Royal Insttute of technology Centre of Excellence for Scence and Innovaton Studes (CESIS)

2 The Economc Effcency of Swedsh Hgher Educaton Insttutons Zara Daghbashyan Dvson of Economcs CESIS, KTH Emal: Abstract The paper nvestgates the economc effcency of hgher educaton nsttutons (HEI) n Sweden to determne the factors that cause effcency dfferences. Stochastc fronter analyss s utlzed to estmate the economc effcency of 30 HEI usng both pooled and panel data approaches. HEI specfc factors such as sze, load, staff and student characterstcs as well as government allocatons are suggested to be the potental determnants of economc effcency. The results suggest that HEI are not dentcal n ther economc effcency; though the average effcency s hgh, they do perform dfferently. Ths varaton s explaned by the jont nfluence of HEI specfc factors; the qualty of labor s found to be hghly sgnfcant for the cost effcency of Swedsh HEI. JEL classfcaton: C21, C24, I121 Keywords: Cost effcency, Stochastc Fronter Analyss, Unverstes 1

3 1. Introducton Rasng educatonal standards as means of attanng compettveness and growth has been n the agenda for more than ffteen years n Sweden and nternatonally. Accordng to educatonal statstcs from Sweden the number of students n hgher educaton rose by 52% between 1995 and For Sweden, a country wth a publcly fnanced hgher educaton system, the ncrease n student populaton means an ncrease n government expendtures. Currently about 1.6% of the Swedsh GDP s devoted to hgher educaton and research, whch provdes employment to 64,300 people. Ths makes the hgher educaton sector mportant not only as a source of human captal producton and development but also from economc consderatons. The queston that s asked n ths paper s how effcently operates the Swedsh hgher educaton sector? Are the tax-payers resources allocated to the hgher educaton sector utlzed effcently? Do HEI operate at the same level of effcency or do they exhbt dfferent economc behavour? What drves the economc effcency of HEI? Before gong further t s worth gvng the defnton of the economc effcency, whch s the major concern of ths paper. Modern effcency measurement began wth Farrel (1957), who defned the economc effcency as the ablty to obtan maxmum output from the resources avalable (techncal effcency) and to choose the best package of nputs gven ther prces and margnal productvtes (allocatve effcency). The classcal mcroeconomc theory assumes that frms and nsttutons operatng n a free market exert maxmum effort to maxmze ther profts/mnmse ther costs and hence operate at 100% effcency,.e. they produce maxmum output from the gven nputs and use the best combnaton of nputs. However, the evdence from practce does not always support ths. Some frms, especally those operatng as nonproft organzatons, tend to devate from the predcted behavor and are hence regarded as neffcent (James, 1990). There may be many reasons for such dvergence from the optmal behavour and dfferences n effcency. Emprcal nvestgaton nto the determnants of effcency dates back to the early 1990s. For nstance Lovell (1993) stated that dentfyng the factors that explan dfferences n effcency s essental for mprovng the results, but that, unfortunately the economc theory does not supply a theoretcal model of determnants of effcency. However Caves and Barton (1990) suggested that several studes have developed a strategy for dentfyng the determnants of effcency whch can be grouped nto the followng categores: () external factors, () nternal factors, () ownershp structure (publc vs. prvate). For hgher educaton nsttutons all the factors affectng the effcency can be grouped nto HEI 2

4 specfc or nternal factors, staff and student specfc or external factors. There s no dstncton between prvate and publc unverstes for the Swedsh HEI because the Swedsh hgher educaton s manly publcly fnanced. Among HEI specfc factors that may nfluence the effcency of HEI I dstngush the sze and load as well as the share of government support n revenues of each HEI. Staff characterstcs reflectng the qualty of teachng/research personnel as well as the age of actve personnel are consdered as staff specfc factors. Student characterstcs such as qualty and foregn background are chosen to reflect student specfc factors. Thus, the focus of ths paper s on the estmaton of the economc effcency of hgher educaton nsttutons of Sweden to see f the HEI operatng n the same market and beng regulated by the same legslaton exhbt dfferent effcency and to whch extent ths dfference can be explaned by HEI specfc factors, staff and student specfc characterstcs. The analyss s conducted for 30 HEI of Sweden usng the stochastc fronter methodology. Pooled and panel data models are estmated to check for consstency of results. The results suggest that though the majorty of HEI operates wth the economc effcency above average there s consderable varaton n ther performance. Ths varaton s the result of the jont nfluence of factors such as labor and student characterstcs, HEI sze and government fundng. The mpact of the labour qualty s found to be the most mportant determnant of economc effcency. 2. Lterature revew The prevous lterature focused on hgher educaton effcency can be dvded nto two man groups - those usng Data Envelopment Analyss (DEA) and those choosng Stochastc Fronter Analyss (SFA). Both are fronter methodologes amed at the estmaton of producton/cost fronter and effcency; however they dffer n the underlyng assumptons. The advantages and dsadvantages of both methods are now well recognzed: n SFA the functonal form of the effcent fronter s pre-defned or mposed a pror, whereas n DEA no functonal form s pre-establshed but s calculated from the sample of observatons n an emprcal way. DEA s a determnstc method and assumes that all devatons from the effcent fronter are due to neffcency, whereas n SFA the dvergence from the effcent fronter occurs due to the neffcency and some random shocks out of agents control. No method s strctly preferable to any other; the choce of the methodology depends on the specfc stuaton where some estmaton technque proves superor. 3

5 Several studes have appled DEA to nvestgate the relatve effcency of hgher educaton nsttutons (Johnes & Johnes (1993), Johnes (2006), Glass, McKllop &Hyndman (1995) Abbot & Doucoulagos (2003) etc). These studes ndcate that there are varous degrees of techncal and/or cost effcency n hgher educaton nsttutons and that unverstes are not homogenous n ther performance. In an attempt to explan the varaton n the effcency of the unverstes some DEA studes also report scale effcency scores (Abbot & Doucoulagos (2003), others (Ahn et. Al., (1988)) compare effcency scores for dfferent ownershp structures. Glass et al. (1988), Madden et al (1997) use two-stage methods to evaluate the research fundng polces on the level of effcency. The studes that employed SFA as a method to estmate the economc effcency of hgher educaton nsttutons are more dverse. They dffer not only n the choce of the functonal form but also n the dstrbutonal assumptons on the neffcency term and hence the determnants of neffcency. For nstance, Izad et al (2001) use fronter estmaton technques to estmate a CES cost functon under the assumpton of half normally dstrbuted effcency wth zero mean and fnd that sgnfcant neffcency remans n the Brtsh hgher educaton system. Usng stochastc fronter methodology Robst (2001) nvestgates the mpact of state appropratons on the cost effcency of publc unverstes and fnds that unverstes wth smaller state shares are not more effcent that unverstes wth hgher state shares. Stevens (2001) estmates the cost effcency for a group of Englsh and Welsh unverstes and fnds that there s neffcency n hgher educaton sector. Ths study s unque n the sense that t models the neffcency as a functon of staff and student characterstcs as effcency determnants and fnds that proportons of professoral staff have a postve effect on effcency, whereas the proporton of staff that s over-ffty effects the effcency negatvely. Argung that effcency estmates maybe senstve to the choce of methodology McMllan & Chan (2006) made a comparson of results from applcaton of both DEA and SFA methods for a sample of 45 Canadan unverstes. They found consstency n the relatve rankng of ndvdual unverstes for hgh effcency and low effcency groups. Though all these studes gve consderable nsght about the operaton of hgher educaton nsttutons and suggest that HEI dffer n the effcency of ther operaton, they do not fully address the ssue of effcency determnants. Ths study s an attempt to estmate the effcency of hgher educaton nsttutons whle tryng to explan the reasons that mght cause heterogenety n HEI performance. 3. Methodology 4

6 Whle choosng a method for the estmaton of the economc effcency of Swedsh HEI I gve preference to SFA due to the possblty to account for random shocks and make an absolute estmate of effcency. In DEA the effcency estmates are relatve and there are no statstcal tests to check for the presence of neffcency. The applcaton of SFA requres choosng a functonal form for the respectve cost functon and makng dstrbutonal assumptons about the neffcency term under the assumpton that all unts under consderaton are cost mnmsers. Whle the actvty of hgher educaton nsttutons s more often targeted at the pursut of excellence and prestge maxmzaton (Robst, 2001), ths does not preclude them from mnmzng ther costs gven the same aspratons for excellence and prestge and the cost mnmzaton behavor seems to be plausble n the hgher educaton sector context Functonal form The exstng lterature suggests a wde varety of functonal forms to descrbe the costs of mult-product organzatons, to whch HEI belong. It s now well recognzed that the actvty of HEI s targeted at teachng, research and communty servce and HEI should be treated as mult-product organzatons. The tradtonal multple-output cost functons relate costs to the multple outputs, nput prces and some exogenous varables havng mpact on the cost functon: C c( y, w, z;,, ) (1.1) where C s the total cost, y s a vector of output varables, w represents the vector of nput prces and z s a vector of exogenous factors; β,γ,θ are the respectve parameters to be estmated. To estmate the relatonshp between the cost and the dependent varables some functonal form should be assumed. The decson whch functonal form to choose for the emprcal analyss s usually not straghtforward snce the true shape of the functon s unknown. Wthn the context of the problem the form should be as general as possble and mpose the fewest possble a pror constrants. Some functonal forms suggested n the lterature are more restrctve, mposng several restrctons upon parameters of the cost functon (Cobb-Douglas, CES and Leontef), whle others whch are more flexble should be checked for meetng the propertes of cost functons (Translog, Quadratc, Generalzed Translog). Many authors prefer to use flexble functonal forms because they are less restrctve and provde local second-order approxmaton to any well-behaved underlyng cost functon; however the estmaton of flexble functonal forms requres a large sample sze, whch s not always possble. Moreover, multcolnearty among the regressors s lkely to 5

7 lead to mprecse estmates of model parameters. As noted n Kumbhakar and Lovell (2000) the beneft of flexblty s lkely to be offset by the cost of statstcally nsgnfcant parameter estmates. Dfferent functonal forms have been used to estmate the costs of HEI. Thus, McMllan and Chan (2006) used Cobb-Douglas functonal form for Canadan HEI, Izad et all (2000), estmated CES functon for Brtsh HEI, Robst (2001) estmated translog cost functon for South Carolna HEI, whle Koshal and Koshal (2000) preferred a flexble quadratc form. Ther choce s manly motvated by the data character and sample sze. In ths paper I follow McMllan and Chan (2006) and use Cobb-Douglas functonal form for the estmaton of the cost functon of Swedsh HEI n vew of the small sample sze. The major drawback of Cobb-Douglas s the assumpton that all elastctes of substtutons are equal to 1, whch mght not be the case n realty. However, the great vrtue of the Cobb- Douglas form s that ts smplcty enables to focus on the neffcency problem whch s the major concern of ths analyss. Moreover, t s less data demandng Stochastc Fronter Analyss The estmaton of the cost functon by tradtonal OLS would allow fndng the average cost functon under the assumpton that all unts exhbt the same effcency of operaton. Ths would be n complance wth the tradtonal mcroeconomc theory, whch assumes that frms and nsttutons are proft-maxmzers/cost-mnmsers and hence they make maxmum effort to produce maxmum output wth mnmal costs. However the emprcal studes suggest that n realty not all frms are always so successful n solvng ther optmzaton problems. Whle some frms operate on the fronter and earn hgh profts, others lag behnd and barely survve (Badunenko et al, (2008)). Such organzatons tend to devate from the predcted optmal behavour, and hence are treated as neffcent. Effcent frms operate on the fronter; they produce maxmum output from the gven nput (techncal effcency) and use the optmal nput proportons (allocatve effcency). Whereas neffcent frms dverge from the optmal behavour and operate beneath the fronter. Stochastc fronter analyss allows buldng cost models wth consderaton of unt specfc neffcency and exogenous shocks beyond the control of analysed unts. It allows modellng the producton and cost structure of frms and nsttutons exhbtng dfferent pattern of effcency. The classcal cost functon n SFA C c( y, w, z ;,, )exp( v u ) conssts of three parts a determnstc fronter c( y, w, z;,, ) common to all producers (n our case HEI), a 6

8 producer specfc random part v, whch captures the effects of random shocks on each producer, and an neffcency component u.the frst error component v s ntended to capture the effect of statstcal nose, whereas u s the non-negatve cost neffcency component, whch s the product of techncal and allocatve neffcency. The unts operate on the fronter or beneath f ther neffcency component u s 0 or u>0 respectvely. If all the unts operate on the fronter then u =0 for all the unts and there s no place for neffcency Incorporatng exogenous nfluences on effcency The analyss of cost effcency has two man components. The frst s the estmaton of the stochastc fronter that serves as a benchmark aganst whch to estmate the effcency wth whch producers allocate ther nputs and outputs under some behavoural assumptons. The second component concerns the ncorporaton of exogenous varables, whch are nether nputs nor outputs, but whch nonetheless exert an nfluence on the performance. As noted ín Kumbhakar and Lovell (2000), the objectve of the second component s to assocate varaton n producer performance wth varaton n exogenous varables characterzng the envronment n whch producton occurs. Examples nclude the qualty of nput and output ndcators, varous manageral characterstcs, ownershp structure etc. These factors may nfluence the cost functon ether drectly or ndrectly through effectng the effcency wth whch nputs are converted nto outputs. Kumbhakar, Gosh and McGulkn (1991) developed a model for estmatng both fronter and effcency terms wth exogenous varables servng as determnants of effcency. The model was further modfed by Battese and Coell (1992, 1995) for panel data wth tme varyng neffcency and Ptt and Lee (1991) for tme nvarant neffcency. 4. Varable selecton As mentoned before the data tradtonally requred for a cost effcency analyss nclude output varables, nput prce varables and exogenous varables havng an nfluence on costs ether drectly or through an neffcency component. In ths secton the varables that should be ncluded n the cost fronter model as well as those that can serve as neffcency determnants are dscussed Inputs and outputs of HEI The choce of the unversty output varables to be ncluded n the analyses s of specal concern. HEI output s usually charactersed as educaton, research and communty servce 7

9 and as noted n McMllan and Chan (2006), nether teachng nor research s partcularly well measured and servce s usually entrely mmeasurable. There s consderable dsagreement among economsts of hgher educaton as to what s the best way to quantfy the output of educaton. However the most common measure of educaton output used n the lterature s the full year equvalent number of students n undergraduate and graduate educaton. Another alternatve s to use the number of graduates; however ths ndcator reflects the outcome of HEI operaton n precedng years and s less precse. In ths study I use the number of full year equvalent students n humantes, medcne and techncal scences to dstngush the heterogenety of nsttutes n specalzaton and hence dfferences n costs ncurred for educatng graduates n dfferent felds. Such dstnctons have been used by Izad et al, (2002), Johnes (1998), Stevens (2001). The number of PhD students s taken as a separate output ndcator to dstngush between undergraduate and graduate educaton. HEI are not homogonous n the qualty of students that are admtted and graduated, hence the qualty of students and graduates s an mportant factor to be ncluded n the model. Gven the same qualty of entrants, t mght be more expensve to graduate students wth hgher qualty. At the same tme the qualty of students beng admtted may also be mportant snce less effort s requred to educate them. Prevous studes have rarely taken nto account the qualty of students enrolled n HEI. An excepton to ths s Koshal and Koshal (1999), where Student Apttude Test was used to control for the qualty of admtted students and Stevens (2001), where A level scores are used as an ndcator of student qualty. Although these ndcators serve as good proxes for student qualty ths data are dffcult to get for the Swedsh HEI, snce accordng to the Swedsh law no entry exams are requred and hence there s no common ndcators for the newly enrolled students. I suggest another ndcator of student qualty, whch s the competton the entrants face for admsson to HEI. I assume that the hgher the competton that unversty entrants face for gettng admtted to unversty the more sklled they are. In condtons of low competton unverstes are more lkely to admt students wth lower qualty and hence ths ndcator can serve as a proxy for the qualty of students admtted. Furthermore, the qualty of teachng output that s the qualty of unversty graduates s another aspect that requres specal care. For nstance, consder two nsttutons wth the same number of students where one provdes excellent educaton and graduates whle the other provdes only a standard educaton. The falure to ncorporate ths qualty factor may result n msleadng evaluaton and comparson. Nevertheless to my knowledge the only study that 8

10 models the qualty of graduates s Stevens (2001), n whch the proporton of frst and upper second class degrees s suggested as a consstent measure of degree qualty. Other potental ndcators of graduates qualty mght be the ntal salary of graduates normalzed by felds or the employment possbltes after the graduaton. The latter s used n ths study to control for the qualty of HEI graduates. It s assumed that the hgh lkelhood of employment s a sgn of hgh qualty of graduates ceters parbus. Of course, one can argue that the success on the labour market s also lnked to other factors such as personal characterstcs and labor market demand. However gven the same labor market condtons and personal characterstcs the frst employment after graduaton s more lkely to be due to qualtatve educaton and the further promoton due to personal characterstcs. The dffcultes n measurng the research output of HEI have been dscussed n many studes. The research produced n HEI s an ntangble asset and ts valuaton s not an easy task. Emprcal studes mostly use ether publcaton counts or research expendtures; however both of them have shortcomngs. For nstance, usng feld normalzed number of journal publcatons suggested by some authors allows controllng for the qualty and feld of research, however as argued n many studes the research output of HEI s not lmted to the journal publcatons. Conference papers, book revews, patents are all vable outputs and smply choosng one bases the results. At the same tme research fundng (Robst (2001), Abbot & Doucoulagos (2001)) chosen as ndcator of research output fals to account for the qualty and feld dfferences. The researchers usng research fundng as a measure of research output argue that the ablty of HEI to generate such funds s closely correlated wth ts research output (Cohn, et al (1989). The deal output measure would nvolve a weghted measure for dfferent types of research output and qualty, however specfyng the weghts a pror based on value judgements could be erroneous. In ths paper the research output of HEI s represented by total research fundng despte all the shortcomngs of ths approach. The prces for nputs to the producton process are the next category of varables to be ncluded n the model. The average salary of HEI personnel s taken as the prce pad for labour nput. It could be desrable to dstngush between the prces pad to dfferent labor categores, but ths nformaton s dffcult to obtan. The prce pad for captal nputs,.e. facltes and equpment, s not ncluded n the analyss due to the lack of data. Ths s a common problem, and as a result t s unusual for captal nput measures to appear n HE cost studes (McMllan & Chan, 2006) Exogenous varables 9

11 In addton to the man nput output categores dscussed above, some exogenous varables that affect total costs ether drectly va nfluencng the cost fronter or ndrectly va effectng the neffcency component should be ncluded. The exogenous varables effectng the actvty of HEI are separated nto () () () HEI specfc factors such as HEI sze, proxed by the number of full-year equvalent students; load per teacher, defned as the rato of full tme student equvalent to the number of teachng and research personnel; the proporton of government fundng n the total amount of HEI revenues and the share of research fundng that comes from external sources staff specfc factors such as the share of professors n teachng research personnel; the share of teachng research personnel aged above 50 student characterstcs such as student qualty dscussed above, the share of students wth foregn background; the share of students aged below 25. The effect of these varables may work n a number of ways. For nstance the proporton of professors taken as a measure of staff qualty would ncrease HEI costs, at the same tme t mght contrbute to the more effcent operaton havng mpact on the educaton output n terms of quantty and qualty. The same refers to the sze of HEI proxed by the number of full-tme students; whle the sze of HEI s expected to ncrease costs, ts effect on economc effcency s not clear. If HEI operate under ncreasng return to scale, whch s the predcton of some studes (Koshal et al, 2000) ths effect would be postve. The mpact of student specfc varables such as the proporton of students wth foregn background s also hard to predct. Whle enrolment of foregn students may be lnked wth extra costs t may postvely effect the effcency provded that foregn students have hgher qualty. The hgher the qualty of students wth foregn background the hgher the lkelhood that the extra costs would be compensated and would not effect the effcency. These varables wth double effect are ncluded n both cost fronter and effcency parts of the model. The remanng envronmental varables, whch are beleved to have no drect nfluence on the cost fronter, are ncluded n the effcency model only. Thus, followng Robst (2001) and Kuo& Ho (2007) I nclude the proporton of government fundng n the effcency model. Currently 88% of HEI revenues are fnanced by the Swedsh government and the rest comes from external sources. The government allocaton of funds s based on student performance ndcators for undergraduate educaton and agreements on 10

12 fundng of graduate educaton and research actvtes. Thus, though the hgher educaton sector s manly publcly fnanced, the share of government support n the total revenues vares across HEI. Interestngly the fndng from Robst (2001) for South Carolna HEI that unverstes wth smaller state shares are no more effcent, contradcts the results of Kuo & Ho (2007) for Tawan publc unverstes. The load per teacher specfc to each HEI s ncluded n the effcency model. Whle the ncrease n ths ndcator would probably decrease total costs, t can have an opposte effect on the qualty and thereby nfluence the economc effcency. Followng Stevens (2001) the proporton of young students and elder teachers s ncluded n the neffcency model to control for demographc effects. The qualty of HEI entrants proxed by ntake qualty ndcators dscussed above and the proporton of research fundng comng from external sources are ncluded to control for qualty dfferences and examne ther mpact on cost effcency. 5. Data Currently the Swedsh HEI conssts of 14 state controlled unverstes and 15 unversty colleges 12. In addton there are 3 prvate unverstes wth the rght to examne research students. The analyss s conducted for 30 HEI usng data from (2 unverstes are wthdrawn from the analyss n vew of the small number of students.) The data used for the analyss s to a large extent drawn from the database of Swedsh Natonal Agency for Hgher Educaton, whch contans detaled nformaton on students, personnel and economy. The descrptve statstcs of all the data used for the analyses dvded nto fve groups are presented n table 1: Table 1: Varable descrpton Descrptve statstcs of key varables Abbrevaton Mean St.Dev. Mn Max Output Indcators Full-year equv. number of undergraduate students TotUndSt Full-year equv. perform. of undergr. stud. n medcne MedUndSt Full-year equv. perform. of undergr. stud. n humanty HumUndSt Full-year equv. perform. of undergr. stud. n techn scences TechUndSt Number of PhD Students (unverstes only) PhD Research expendture (ths. SEK) ResFund Excludng those unversty colleges devoted to arts, sports, pedagogy and the lke. 2 In Sweden unversty colleges have no rght to graduate PhD students. 11

13 Input Prce Average annual salary (ths. SEK) AvSalary Student characterstcs Number of applcants per place n HEI (admsson) IntakeQ 2,5 1,2 0,6 7,1 % of students aged below 25 STB % of students wth foregn background ForBack % of graduates employed after 1-2 years of graduaton EmplL Staff characterstcs % of professors n teachng and research personnel Profess % of teachng and research personnel aged above 50 TA Number of students per teacher Load Costs* Total HEI expendtures (ths. SEK) TotalCost % of government allocatons n total costs GovAlloc (%) % of research fundng from external sources ResFundExt(%) Other Dummy for HEI wth the rght to graduat PhD students ResD 0 1 *All the monetary varables ncluded n the model have been deflated usng producer and mport prce ndex wth 2005 as base year. It s worth notng that the Cobb-Douglas structure of the cost functon chosen for the analyss assumes that all output ndcators as well as prce and total cost ndcator should be n the logarthmc form. However the number of PhD students, whch s one of the output ndcators used, s 0 for 10 out of 30 HEIs ncluded n the analyss. To solve the problem I use the value of 1 for HEIs graduatng no PhD students and follow the procedure suggested by Battese (1997),.e. by usng a dummy varable assocated wth the ncdence of zero observatons, the approprate parameters of Cobb-Douglas functons can be estmated n an unbased way. 6. Emprcal model Guded by the dscusson above the followng emprcal model (n the fashon of the model suggested by Kumbhakar, Ghosh and McGukn (1991)) s used for the estmaton of multdmensonal cost functon of HEI. 3 lntc lnstud ln PhD ln R F w AvSal GradQ IntakeQ 0 j j 1 ForBack Proff Re sd v u (1.2) where v s the random error nose component, whch s assumed to be normally dstrbuted wth zero mode. The second error term u captures the effects of economc neffcency and has truncated normal dstrbuton, wth a systematc component assocated wth the exogenous varables and a random component 12

14 u TStud Load GovFund Proff TA50 SB25 Forback IntakQ RFExt 8 9 (1.3) If t s assumed that and v are dstrbuted ndependently of each other and the regressors the parameters of the model can be estmated by one-stage MLE (for more detals see Kumbhakar & Lovell, 2000). After the estmaton an estmate of economc neffcency s provded usng ether JLMS (Jondrow et al., 1982) technque or Battese and Coell (1988) pont estmator. Once pont estmates of u are obtaned, the estmates of effcency of each unt are calculated as ^ CE u exp( ) (1.4) The model can be extended to panel data wth tme-varant and tme nvarant neffcency terms (Battese and Coell (1995)) and Ptt and Lee (1991) models respectvely. The man advantage wth panel data s that t allows gettng unbased and consstent estmates whereas the cross-secton analyss does not guarantee the consstency of results. Panel data wth TI neffcency s used when the effcency s consdered systematc and hence u s treated as frm-specfc constant, whereas tme nvarant models allow effcency to change over tme. 7. Results 7.1. Pooled data The results of maxmum lkelhood estmaton of the stochastc fronter Cobb-Douglas functons for the pooled data for academc years are summarzed n Table2. Three dfferent model specfcatons are presented. The neffcency term ncluded n all three models has truncated normal structure wth a systematc component, whch s a functon of HEI specfc varables, staff and student characterstcs. The models have the same structure for the cost fronter functon and dffer n varables explanng neffcency. The frst model s the general nested model aganst whch other models wth some varables excluded are tested. Table 2: Stochastc fronter coeffcents for pooled data Specfcaton 1 Specfcaton 2 Specfcaton 3 Cost fronter functon Intercept 4,681*** (0,924) 5,371*** (0,799) 6,586*** (0,623) lnresfund 0,495*** (0,025) 0,529*** (0,022) 0,525*** (0,020) lnmedundst 0,003 (0,006) 0,027*** (0,006) 0,027*** (0,005) lntechundst 0,135*** (0,018) 0,116*** (0,013) 0,115*** (0,012) lnhumunds 0,059*** (0,017) -0,007 (0,013) -0,024** (0,012) lnphd 0,067*** (0,024) 0,093*** (0,019) 0,103*** (0,020) lnavsal 0,205 (0,142) 0,074 (0,115) 0,096 (0,091) Empl -0,002 (0,001) -0,003 (0,002) -0,004*** (0,001) 13

15 InatakeQ -0,704 (0,003) -0,000 (0,000) -0,000** (0,000) ResD -0,305*** (0,081) -0,397*** (0,074) -0,485*** (0,071) Profess 0,011*** (0,005) 0,0137*** (0,003) 0,019*** (0,003) Forback -0,011*** (0,004) 0,000 (0,002) 0,000 (0,002) Ineffcency model Intercept 0,147 (0,513) -0,143 (0,236) -0,196 (0,249) Load -0,033 (0,025) 0,014* (0,008) 0,015* (0,008) TotUndSt 0,000 (0,000) 0,000* 0,00,204** (0,103) GovAlloc -0,006 (0,005) -0,000 (0,002) ResFundExter -0,003 (0,004) -0,003** (0,002) -0,002* (0,001) Profess -0,058** (0,031) -0,051*** (0,015) -0,054** (0,023) TA50 0,026*** (0,012) 0,010** (0,004) 0,015** (0,006) STB25-0,007 (0,008) IntakeQ -0,000 (0,003) Forback 0,038*** (0,018) 0,013** (0,006) 0,008** (0,005) Varance parameters for compound error Lambda 1,378*** (0,571) 1,796*** (0,507) 2,433*** (0,945) Sgma 0,126*** (0,025) 0,109*** (0,010) 0,103*** (0,009) Loglkelhood Note: standard errors are presented n parenthess *p<0,1 **p<0,05 ***<p<0.01 Lambda parameters reported n the table provde an ndcaton of the relatve contrbuton of neffcency and random error terms to the whole error component ( v u ). These coeffcents are sgnfcantly dfferent from 0 n all three models suggestng that the dvergence from the fronter cost functon s to a great extent explaned by heterogeneous neffcency. LR test for comparng three dfferent model specfcatons suggests the thrd model, whch has the hghest lkelhood value. Nevertheless the estmates of coeffcents from three models are qute smlar. Not surprsngly the results suggest that costs ncrease wth the number of students and that the educaton of students n techncal scences s more costly. The second and thrd models show that unverstes wth hgher number of students n humantes wll have lower costs, whch seems reasonable. Though the number of PhD students s suggested to ncrease costs the dummy varable for research unverstes (that are allowed to graduate PhD students) s negatve. Ths mght mean that HEI wll ncur lower costs, f they are allowed graduatng PhD students, snce the same facltes and staff used for undergraduate educaton can be utlzed. Besdes PhD students are also supposed to be nvolved n teachng actvtes thereby decreasng unversty labor costs. The coeffcent for the average salary s postve n all three models, but t s not sgnfcantly dfferent from 0, whch s surprsng. 14

16 The proxy for the graduates qualty,.e. the fracton of graduates employed after two years of graduaton s nsgnfcant n the frst two models. Though t gets sgnfcant n the thrd model the sgn s stll negatve, meanng that t costs less to graduate hgher qualty students. One explanaton s that the qualty of graduates proxed by the lkelhood of employment depends on both teachng effort and student personal characterstcs and teachng of smart students wth hgher chances of success on labor market may be less expensve. By the same token the coeffcent for the student ntake qualty s negatve suggestng that t costs less to educate smart students. Gong further, the results suggest that the more professors the HEI employ the more costly t wll be, whch seems to be reasonable. Turnng the attenton to the neffcency part of the table whch s the man concern of ths study one can see the potental determnants of neffcency dfferences among HEI. The coeffcents for the load per teacher and HEI sze are both postve and sgnfcant n the second and thrd models. It suggests that the hgh load negatvely effects effcency through decreasng the qualty of teachng, whch seems to be plausble. At the same tme the results suggest that bg HEI are less effcent. Ths could be due to dffcultes n coordnaton of actvtes, scale effects. Interestngly, whle comparng the rankng of unverstes worldwde wth ther sze Andersson et al. (2009) found clear ndcatons that smaller unverstes are more lkely to be hghly ranked and perhaps ths has to do wth the effcency of operaton. The coeffcent for the proporton of government allocatons n HEI ncomes s nsgnfcant, meanng that government allocatons do not affect the effcency of unversty operaton. One explanaton s that the government allocates funds based on students performance, and hence no unversty s prvleged. On the other sde HEI also get government fundng for research actvtes, whch s not performance based, moreover non-research unverstes do not get fundng for research actvtes at all. Interestngly the share of external research fundng from the total research fundng s negatve and sgnfcant suggestng that HEI beng able to attract more external money for research are more effcent. In any case, the results suggest that unverstes wth hgher shares of publc support are no less effcent The coeffcents for staff characterstcs, represented by the share of professors n the total research/teachng staff and the share of teachng/research staff aged above 50, suggest that the qualty of staff proxed by the share of professors postvely effects the effcency. Unverstes employng more professors wll be more effcent ceters parbus. At the same tme the age of teachng and research personnel ncreases neffcency. Senor teachers are less lkely to contrbute to effcency. 15

17 From all three student characterstcs ncluded n the model, foregn background s the only one whch s sgnfcant. Accordng to the results student background negatvely nfluences effcency. HEI enrollng more foregn students wll probably be less effcent ceters parbus. Ths seems to be n lne wth the postve coeffcent for the foregn background n the cost fronter part of the model, meanng that enrollng more students HEI ncur more costs whch n turn effects ther effcency Panel data In the prevous secton the results from the estmaton of HEI cost functon usng pooled data analyss was presented The nformaton on the panel character of the data was not ncluded n the model. In ths secton I extend the analyss addng new nformaton to the model and estmate the fronter cost functon for the panel data usng Battese and Coell tme varant and Ptt and Lee tme nvarant models. As mentoned before Battese and Coell model assumes that neffcency changes over tme, whereas Ptt and Lee model assumes no varaton n neffcency over years. Snce the tme span ncluded n the analyss s 5 years, both cases are possble. Hence I estmate both models and use statstcal tests to dscrmnate between the models. Student characterstcs, ntake qualty and age, whch are strongly nsgnfcant n the pooled models, were excluded from the effcency model Table 3: Stochastc fronter coeffcents for panel data models Cost fronter functon Specfcaton 1 (TV) Specfcaton 2 (TI) Intercept 6,59*** (1,59) 4,73*** (0,856) lnresfund,53*** (0,041),48*** (0,033) lnmedundst,027*** (0,004) 0,01 (0,013) lntechundst,115*** (0,009),130*** (0,029) lnhumunds -0,024** (0,012),05* (0,026) lnphd,104*** (0,018),095*** (0,015) lnavsal -0,098 (0,192) 0,136 (0,13) Empl -0,004 (0,002) 0,001 (0,003) InatakeQ 0,0001 (0,001) 0,006 (0,009) ResD -0,487*** (0,096) -0,328*** (0,109) Profess,020*** (0,002),013*** (0,004) Forback 0,001 (0,003) 0,004 (0,004) Ineffcency model Intercept -0,196 (0,996) -4,33 (9,07) Load 0,016 (0,026) -0,55*** (0,13) TotUndSt 0,000 (0,000) -0,000 (,000) GovAlloc -0,001 (0,013),226* (0,133) Profess -0,054*** (0,019) -0,462** (0,162) TA50 0,015 (0,009) 0,035 (0,122) Forback 0,008 (0,016) 0,15 (0,184) ResFundExter -0,003 (0,003) -0,009 (0,05) 16

18 Varance parameters for compound error Lambda 2,432*** (0,133) 2,44* (1,319) Sgma,096*** (0,000) 0,11*** (0,035) Eta parameter for tme varyng neffcency Eta 0,010 (0,020) Loglkelhood *p<0,1 **p<0,05 ***<p<0.01 The estmated eta coeffcent whch ndcates tme varance n the neffcency component s statstcally nsgnfcant, suggestng no varaton n the neffcency term over tme. Whereas lambda coeffcents from both models are sgnfcantly dfferent from zero wtnessng neffcency varaton among HEI. The sgns and sgnfcance of estmated coeffcents for the fronter cost functon are close to the results of the pooled models. The only varable that s statstcally sgnfcant n both neffcency models wth panel data s the fracton of professors n teachng/research staff. As before ths ndcator s negatve meanng that the unverstes employng more professors operate more effcently. In Ptt and Lee model wth tme nvarant neffcency the load per teacher s negatve and sgnfcant, whch contradcts the fndngs from the pooled data models. Ths maybe due to non-lnear relatonshp between the load and neffcency, where the load contrbutes to the decrease of neffcency to some optmal pont and then operates n the opposte drecton. Furthermore, government allocatons are estmated to be sgnfcantly postve n Ptt and Lee model, suggestng that unverstes havng more publc support are less nclned to operate effcently. It s worth notng that ths varable was estmated to be nsgnfcant n models wth pooled data. 8. Cost effcency estmates from dfferent model specfcatons In ths secton the effcency scores from pooled and panel data models are presented. Table 3 demonstrates the descrptve statstcs for the effcency scores from 3 three dfferent models. Though the mnmum and maxmum values are qute dfferent the standard devaton n all three models s relatvely smlar. Table 4: Dscrptve statstcs for cost effcency Pooled Model BC Model PL Model Max 0,97 0,99 0,98 Mn 0,70 0,56 0,54 Mean 0,87 0,88 0,79 St.Dev. 0,08 0,13 0,11 17

19 Effcency score On average the correlaton coeffcent for the neffcency scores from 3 models s 0.82, Fgure 1 demonstrates the convergence of results from pooled and panel data models. Though the effcency scores are dfferent across the models, ther relatve rankng s qute smlar. Fgure1: Effcency estmates n pooled and panel data models 1,2 1,0 0,8 0,6 0,4 0,2 0,0 UU LU GU SU UMU LIU KI KTH LTU SLU KAU VXU ÖU MIU HK BTH MAH HEI CTH HHS HJ HB HDA HIG HG HH HKR HS HV MDH SH 11 out of 30 HEI ncluded n the sample operate wth hgh effcency, 14 have an average effcency of operaton, whereas 5 exhbt an effcency below average. Bg HEI such as Stockholm Unverstetet, Chalmers Teknska Högskolan, Uppsala Unverstetet as well as small ones such as Handelshögskolan Stockholm, Södertorns Högskolan, Bleknge Teknska Högskolan and Luleå Teknska Unverstetet are among those ranked hghly effcent. These results ndcate that the sze does not necessarly guarantee economc effcency. One surprsng result s the low effcency of Karolnka Insttutet (KI), whch has a hgh nternatonal reputaton. The comparson of characterstcs of KI wth other HEI n the sample revealed that KI has extremely hgh proporton of foregn students. The results for KI change dramatcally when ths ndcator s vared. Thus, KI becomes the most effcent n the sample when the proporton of foregn students s decreased. Ths could mean that nternatonal prestge and the possblty to attract foregn students costs more, and hence effects the economc effcency gven the qualty of output does not change. In the same token, the proporton of foregn students n the HEI havng got the hghest effcency scores was below average. Thus, some HEI havng hgh-rankng by academc crtera are estmated to have low economc effcency, whereas others ranked relatvely low got hgher economc effcency scores. Ths s because academc crtera tradtonally used n buldng HEI rankngs do not account cost aspects and hence can be qute dfferent. Furthermore the cost effcency 18

20 analyss, whch s the subject of ths study, s based on the assumpton that the unts under nvestgaton are cost mnmsers. However, f HEI are more nterested n prestge or excellence maxmzaton, whch s not necessarly the same as cost mnmzaton, they wll get hgh prestge rankng and low cost effcency rankng. 9. Concluson The am of ths study was to examne the cost effcency of Swedsh HEI and fnd the factors that determne t. SFA was appled to the sample of 30 HEI for the academc years to estmate the heterogenety n utlzaton and allocaton of resources. Pooled and panel data approaches were utlzed to check for the robustness of results. The results suggest that Swedsh HEI dffer n ther cost effcency. The estmated effcency of most unverstes s above the mean and only 6 HEI have got effcency estmates below the average. The results also suggest that the effcency of Swedsh HEI dd not change much wthn the perod dscussed. To analyse the neffcency determnants three groups of varables were ncluded n the neffcency model: unversty specfc ndcators, staff and student characterstcs. The fndngs for unversty specfc factors, n partcular load per teachng/research staff, unversty sze and the share of government support n total fundng are ambguous. In models wth pooled data both load and sze have negatve mpact on effcency, whereas these ndcators are not sgnfcant n panel data models. On the contrary government fnancng s sgnfcant and negatve n the model wth tme nvarant neffcency and nsgnfcant n other models. The staff characterstc represented by the fracton of professors n teachng/research staff s found to have sgnfcant mpact on the HEI cost effcency. The results from all the models support the dea that unverstes employng more professors exhbt hgher effcency. The models wth polled data also suggest that young teachers and researchers contrbute more to the HEI performance n terms of economc effcency. As to the student characterstcs, the results suggest that the age and qualty of students do not effect the cost effcency, whereas foregn background s a sgnfcant and negatve factor to cost effcency. Interestngly, foregn background s found to ncrease HEI costs, whch mght be the reason of the negatve nfluence of students wth foregn background on economc effcency. 19

21 The man mplcaton from ths analyss s that HEI subject to the same legslaton and regulatons as well as the partcular statutes, ordnances and regulatons relevant to the hgher educaton sector of Sweden exhbt dfferent economc effcency. Ths neffcency s explaned by the jont effect of factors dscussed n ths study. References 1. Abbot M., Doucoulagos C The effcency of Australan unverstes: a data envelopment analyss. Economcs of Educaton Revew 22 (1) Ahn T., Charnes A., Cooper W Some statstcal and DEA evaluatons of relatve effcences of publc and prvate nsttutons of hgher learnng. Socoeconomc Plannng Scences 22(6): Andersson Å., Beckmann M Economcs of Knowledge: Theory, Models and Measurements. Edward Elgar Publshng 4. Badunenko, M. Frtsch, A. Stephan What drves the productve effcency of a frm? The mportance of ndustry, locaton, RD and sze. CESIS WP Battese G. & Coell T A model for techncal neffcency effects n a stochastc fronter producton functon for panel data. Emprcal Economcs 20: Battese G. & Coell T Fronter producton functons, techncal effcency and panel data: wth applcaton to paddy farmers n Inda. Journal of Productvty Analyss 3, Battese G A note on the estmaton of Cobb-Douglas producton functons when some explanatory varables have zero values. Journal of Agrculture Economcs. 48 (2) Caves R. & Barton D Effcency n US manufacturng ndustres. MIT Press 9. Chakraborty K., Bswas B., Lews C Measurement of techncal effcency n publc educaton: A stochastc and non-stochastc producton functon approach, Southern Economc Journal 67(4): Chambers R Appled producton analyss: A dual approach. Cambrdge Unversty Press 11. Charnes A., Cooper.W, Lewn A., Seford L Data Envelopment Analyss, Theory, Methodology and Applcatons. Boston, MA: Kluwer Academc Publshers 12. Coell J, Rao Ch., O Donnel, Battese G An Introducton to effcency and productvty Analyss. Sprnger 20

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