Economes of scale and scope n Australan hgher educaton Author Worthngton, Andrew, Hggs, Helen Publshed 2011 Journal Ttle Hgher Educaton DOI https://do.org/10.1007/s10734-010-9337-3 Copyrght Statement 2010 Sprnger Netherlands. Ths s the author-manuscrpt verson of ths paper. Reproduced n accordance wth the copyrght polcy of the publsher. The orgnal publcaton s avalable at www.sprngerlnk.com Downloaded from http://hdl.handle.net/10072/35685 Grffth Research Onlne https://research-repostory.grffth.edu.au
1 Economes of scale and scope n Australan hgher educaton Andrew C. Worthngton Helen Hggs 12 Abstract Ths paper estmates economes of scale and scope for 36 Australan unverstes usng a multple-nput, multple-output cost functon over the perod 1998 to 2006. The three nputs ncluded n the analyss are full-tme equvalent academc and non-academc staff and physcal captal. The fve outputs are undergraduate, postgraduate and PhD, natonal compettve and ndustry grants, and publcatons. The fndngs ndcate that ray economes of scale hold up to about 120 percent of current mean output though productspecfc economes of scale hold only for undergraduate teachng. Global economes of scope preval n the sector, ncreasng wth the level of mean output, whle product-specfc economes of scope arse for all outputs except publcatons. A cost effcency ndex constructed usng the sector benchmark ndcates that the unverstes of Ballarat, Southern Cross and Flnders have a hgh level of cost effcency, whle New South Wales, Royal Melbourne Insttute of Technology and James Cook are cost neffcent. Keywords Economes of scale Economes of scope Substtutes and complements n producton Cost effcency Introducton It s patent that the Australan hgher educaton sector has undergone substantal structural change durng the last three decades. At the begnnng of the 1980s, Australa had more than 80 hgher educaton nsttutons operatng n a dual system wth research and teachng-focused unverstes funded on a dfferent bass from teachng-focused nsttutes of technology and colleges of advanced educaton. Wth few exceptons, these nsttutons were comparatvely small (an average sze of less than 8,000 full-tme equvalent students) wth most operatng wthn a comparatvely narrow range of dscplnes and focused on partcular teachng, research, and research tranng roles. However, the Dawkns reforms of the late 1980s brought the ntroducton of a unfed natonal system accompaned by a far-reachng programme of restructurng that saw A.C. Worthngton ( ) H. Hggs Grffth Busness School, Grffth Unversty, Nathan, Queensland 4111, Australa e-mal: a.worthngton@grffth.edu.au
2 Australa s 18 unverstes and 60 colleges combne nto just 38 unverstes, motvated partly by the argument that small nsttutons have unacceptably hgher costs and tertary nsttutons should have a broad educatonal profle. A partal underlyng motvaton was that f large and dverse nsttutons have lower costs, t s because economes of scale (average costs declne wth output) and scope (costs are hgher for specalst provders) arse n hgher educaton. Snce then, the move to a mass educaton system, changes n teachng and research fundng and performance frameworks, and the expanson and development of Australa as a key provder of nternatonal educaton servces, has seen further growth n sze, wth Australan unverstes growng to average 14,000 students n 1998 and more than 18,000 n 2006. However, snce the wdespread program of mergers between 1987 and 1991, relatvely lttle consoldaton has taken place n the Australan hgher educaton sector. Nevertheless, there are now sgns that market and non-market revenue and cost pressures, and the desred polcy outcomes of ncreasng the qualty and dversty of Australan hgher educaton, especally nternatonally, wll focus attenton on further possbltes for structural change wth a new round of allances, mergers, and restructurngs. In evdence of these pressures, the Revew of Australan Hgher Educaton (2008, p. 147) ponted out several problems facng Australa s unverstes, startng wth the fact that over the perod 1995 2005, total natonal expendture on tertary nsttutons n Australa grew more slowly (34 per cent) than GDP (42 per cent) and sgnfcantly less than the OECD average (58 per cent). The clear nference s that Australan unverstes are substantally under-resourced. Just as problematcally, the ncrease n expendture on tertary educaton n Australa durng ths tme was manly due to ncreased prvate expendture, prmarly through student contrbutons and tuton fees. Whle the Revew of Australan Hgher Educaton (2008, p. 171) observed that these new fundng sources had bestowed ncreased operatonal autonomy on unverstes, t also ncreased ther exposure to fnancal rsk, wth 20 per cent of Australa s publc unverstes havng operatng margns of less than 4 per cent n 2007, wth another 15 per cent operatng n defct. Fnally, the Revew of Australan Hgher Educaton (2008) suggested that Australa was losng ground on a range of ndcators of the qualty and performance of ts tertary educaton system, wth unverstes strugglng to do more wth less. There are already sgns these factors are havng an effect on the structure of the sector. For example, n 2005 Edth Cowen Unversty ndependently joned (ultmately frutless) merger negotatons between Western Australa s Murdoch and Curtn unverstes. Lkewse, n July 2008, the Unversty of Canberra and Charles Sturt Unversty confrmed they were explorng
3 the establshment of a system unversty along US lnes followng a smlar May 2008 allance between the Australan Natonal Unversty and the Unversty of South Australa (Healy 2008). Nevertheless, such pressures have been n place for some tme. For nstance, n 2007 the then Federal Mnster for Educaton, Scence and Tranng s recorded as statng that tweakng the prortes of the $46.8 mllon Collaboraton and Structural Reform Fund [would] reward proposals for unversty mergers and campus closures and that Australa had room for perhaps only a dozen fully comprehensve, generc unverstes (Armtage 2007). Concern wth the number of ndvdual campuses has also been longstandng, wth more than half of the more than 150 campuses n Australa havng less than a thousand full-tme equvalent students (Moode 1999). However, ths poston s by no means unversal, wth Unverstes Australa (2008), the peak ndustry lobby group representng Australa s 39 unverstes, n ts submsson to the Revew of Australan Hgher Educaton (2008) contestng that Australa had a relatvely low number of unverstes (per mllon of populaton) compared wth key nternatonal compettors (ncludng Canada, the UK and the US). Unverstes Australa (2008, p. 30) also recommended that nstead of delberately seekng to promote amalgamatons or other radcal structural measures, government polcy settngs should facltate a focus on ndvdual unverstes unque areas of strength and on leavng nsttutons free to pursue greater networkng or lnkages. Both of these postons rely heavly on the contested premse that large unverstes are best able to explot the compettve realtes of global hgher educaton and that the excessve dversfcaton of Australan unverstes across teachng, research, and research tranng s assocated wth substantal costs at both the unversty and sector level. Gven the pervasve belef among some polcymakers and decson makers that larger, more specalsed unverstes are more cost effectve, t s now approprate to revew the avalable evdence on economes of scale and scope n Australan hgher educaton. Astonshngly, lttle contemporary evdence exsts. Throsby (1986) consdered cost data for Australan unverstes and found that average costs fall qute steeply frst, reachng a mnmum level at around 13,000 full-tme equvalent students, before slowly ncreasng. Lloyd et al. (1993) lkewse concluded based on data from the late 1980s that large nsttutons n Australa do not fully exhaust economes of scale, and that these appear to offer greater potental gans than any economes of scope.
4 Usng a nonparametrc approach, Abbot and Doucoulagos (2003) calculated relatve measures of techncal and scale effcency of Australan unverstes for 1995 and concluded that whle there was room for mprovement, unverstes were operatng at a farly hgh level of effcency relatve to each other. These fndngs are comparable to an earler study by Akvran (2001), also usng data from 1995. Overall, these studes tend to support the exstence of economes of scale, as depcted n Fgure 1. As shown, plottng average costs per student completon n Australan unverstes provdes at least some evdence of a U-shaped long-run average cost curve. <FIGURE 1 HERE> Accordngly, the purpose of ths paper s to assess the economes of scale and scope n Australan unverstes. Whle not the only study to examne effcency and/or productvty n Australan unverstes (Throsby 1986; Lloyd et al. 1993; Madden et al. 1997; Akvran 2001; Abbott and Doucoulagos 2003; Carrngton et al. 2005; Worthngton and Lee 2008) t s the only one to focus exclusvely on scale and scope economes at a unversty-level usng recent panel data. Ths wll throw useful lght on the possblty of unverstes attanng effcences through structural change. The paper s dvded nto four man sectons. The second secton brefly dscusses the concepts and sources of economes of scale and scope as they apply to hgher educaton. The thrd secton deals wth the specfcaton of hgher educaton nputs, outputs and costs. The fourth secton focuses on the cost functon specfcaton used to estmate the economes of scale and scope and the ffth secton presents the results. The paper ends wth some concludng remarks. Economes of scale and scope n hgher educaton It s generally consdered that the behavoural assumpton of proft maxmsaton does not well ft unverstes operatng n quas-markets (markets where the government s a prncpal funder but not provder of servces, and retans varyng degrees of control on the number and sze of nsttutons as well as the nputs and outputs employed n the producton process). However, cost mnmsaton s readly applcable to nearly all market and non-market contexts desrous of effcency and effectveness n resource usage and output provson. In contrast to the short run when at least some resource nputs (mostly captal) are assumed fxed, n the long run all resource nputs are varable. A unversty (as the frm) can, for example, alter ts usage of plant and equpment, change management personnel, buld new
5 capacty through buldngs and facltes, close down obsolete facltes or redundant campuses, update ts use of nformaton and other technology, or n any other way modfy ts producton processes and use of resources over tme. These dscussons are mportant because whle the unversty has many concevable optons as to equpment, technology, and the captal labour mx n the long run, once a commtment s made ts stuaton reverts to the short run, where many of these decsons are agan fxed. One possble long-run cost objectve for a unversty s to be n a poston to produce the desred output (or outputs) at the lowest possble cost (or cost mnmsaton). Among other thngs, ths means adjustng ts scale of producton to the most approprate sze. Sometmes dvdng the producton process nto smaller producton unts can result n economes, as evdenced by the dvson of unverstes nto smaller admnstratve unts lke campuses, facultes, schools and departments. On other occasons, enlargng the scale of producton can acheve lower unt costs. Ths can proceed over tme through a contnuum rangng from nternal growth, through to strategc allances, understandngs, and agreements, to formal merger and amalgamaton. Through ths process, unverstes overcome ndvsbltes n factor nputs and the spreadng of fxed costs, avod the costs of nventory stock outs, and gan access to economes n the fxed costs of producton ncludng purchasng, marketng and admnstraton (ncludng human resources and nformaton technology). The producton process for a specfc output s then sad to exhbt economes of scale over a range of output when average cost (AC) (.e. cost per unt of output) declnes over that range (where AC = TC Q ). For long-run average cost (LRAC) to declne, the margnal cost (MC) (.e. the cost of the last unt produced) must be less than overall average costs (where MC = TC Q ). If average cost s ncreasng, then margnal cost must exceed average cost and producton exhbts dseconomes of scale. Generally, dseconomes of scale arse from the ncrease of nput prces, the reducton of ncentves and the growth of bureaucracy, and an ncreasng lack of specalsed resources. Average costs are typcally U-shaped n cost output space, so that the smallest and largest unverstes have equally hgh costs relatve to medum-szed unverstes. That s, on ether sde of the mnmum effcent scale (MES) of producton, costs are rsng so output less than or more than the MES s neffcent from a cost perspectve. In practce, there s much varaton. One possblty s that economes of scale are neglgble and dseconomes domnate at relatvely low levels of output. Elsewhere, economes of scale may be extremely mportant and declne contnuously over a wde range untl output dseconomes are experenced. Ths
6 results n cost effcent outputs for output levels equal to and exceedng the MES. In yet other contexts, the LRAC may be vrtually horzontal over a wde range of output: economes of scale are quckly exhausted though dseconomes are not encountered untl very large levels of output are produced. These L shaped cost curves are ndcatve that small, medum, and largeszed unverstes could operate wth an approxmately equal level of cost effcency beyond the pont of MES where average costs are ether flat or only slghtly ncreasng. The presence of economes (dseconomes) of scale rests on the functonal relatonshp between the costs of producton and the rate of output per perod. In other words, costs = ƒ(output). However, the rate of output s, n turn, a functon of the rate of usage of the resource nputs: that s, output = ƒ(nputs). Snce the producton functon dsplays the relatonshp between nput and output flows, once the prces of the nputs (or factor prces) are known, the costs of a specfc quantty of output can be calculated. Consequently, the level and behavour of costs as a unversty s rate of output changes (as evdenced by the LRAC) depends on two mportant factors: () the character of the underlyng producton functon and () the prces the frm must pay for ts resource nputs. Generally, the frst factor determnes the shape of the cost functon whle the second determnes the level of costs. Consder now a unversty usng L unts of labour (say, academc and non-academc labour) n combnaton wth K unts of captal (both fnancal and physcal) to obtan an output of Q unts such that L + K Q. Now assume that the amounts of labour and captal are ncreased by some arbtrary proporton a wth the expected proportonal ncrease n output gven by b such that al + ak bq. When the change n output s more than proportonal to the change n nput (b > a), ncreasng returns to scale are found. For example f the nputs of labour and captal ncrease by 20%, output rses by 30%. Alternatvely, when the change s less than proportonal to the change n nputs (b < a), the frm experences decreasng returns to scale. An example here would be the labour and captal nputs ncrease by 20% but outputs only rse by 10%. Fnally, where the change n output s proportonal to the change n nputs (b = a) constant returns to scale are present. In ths case, ncreasng nputs by 20% would also result n output ncreasng by 20%. It s often temptng to use the terms economes (dseconomes) of scale (a cost concept) and ncreasng (decreasng) returns to scale (a producton concept) nterchangeably. Whle strctly ncorrect, to yeld economes of scale the producton functon must have some regon of ncreasng returns to scale, and to yeld dseconomes of scale t must have a regon where there are decreasng returns to scale. In fact, the levels of output where economes
7 (dseconomes) of scale and ncreasng (decreasng) returns to scale occur wll exactly correspond when the frm faces constant nput prces as output expands. Ths s most lkely to occur for a relatvely small entty n a compettve ndustry where nput demand by one frm s lkely to be small relatve to total market demand. In other cases, however, where the frm s demand for nputs s large relatve to total ndustry demand, stuatons may arse where economes of scale occur at the same tme that the frm experences constant (or even decreasng) returns to scale. Consder, for example, a unversty wth constant returns to scale n a decreasng cost ndustry. If the nputs (L, K) ncrease by a gven proporton (a), output (Q) wll expand by the same proporton (b) such that b = a (.e. constant returns-to-scale). However, f nput prces declne as Q rses, t follows that the average costs of producng aq must be less than the average cost of producng Q, and long-run average costs must fall (.e. economes of scale). Smlar arguments show that producton can even exhbt decreasng returns to scale and we can stll attan economes of scale so long as the mpact on average costs by the declne n factor prces suffcently offsets the ncreased use of nputs and vce versa. In the above dscusson, a sngle output s consdered. Once multple product producton arses, the presence or absence of complementarty between outputs n producton n a frm becomes mportant. Ths dversty of products (goods or servces) wthn a sngle frm (or unversty n ths case), known as scope, may provde cost advantages n that a sngle unversty producng a gven level of output for product may spend less than a combnaton of several specalsed unverstes. That s, economes of scope arse when t s cheaper n terms of total cost (TC) to produce some level Q of product A n conjuncton wth some level of product B, rather than each separately, TC(Q A, Q B ) < TC(Q A, 0) + TC(0, Q B ). Among frms, ths process often manfests tself as leveragng core competences, competng on capabltes, moblzng nvsble assets, dversfcaton nto related products, and umbrella brandng. In the case of producton n hgher educaton organsatons, the producton process typcally comprses multproduct attrbutes because t produces multple products (undergraduate and postgraduate teachng, research, research tranng, and stakeholder servce) through the sharng and jont utlsaton of nputs ncludng academc and support staff, equpment, buldngs, and so on. Unfortunately, there a number of emprcal dffcultes assocated wth measurng cost economes n unverstes. Frst, the measures of outputs, ncludng teachng, research, and research tranng, may vary n qualty across unverstes. Fortunately, mnmum standards
8 often apply, but a strong correlaton between unversty szes and/or profle and qualty may dstort the results. Second, n quas-markets unconstraned decsons by unverstes do not generate the observatons used for analyss. Government polcy and the allocaton of fundng, however well ntentoned, stll control the mx and level of unversty outputs, and these do not necessarly correspond to effcent outcomes. Fnally, analyss assumes that unverstes are at some equlbrum pont along ther respectve long-run cost functons. Unverstes, n fact, may be at dfferent stages of growth and development and the absence of, say, evdence of dseconomes of scale may smply be because no unverstes n the sector are currently large enough for these dseconomes to apply, not that they do not exst. Specfcaton of outputs, nputs and costs The data consst of annual observatons of 36 Australan unverstes over the perod 1998 to 2006. Ths s the longest and most recent perod where the Commonwealth Department of Educaton, Scence, and Tranng (DEST), now Department of Educaton, Employment and Workplace Relatons (DEEWR), collected consstent data on unversty nputs, outputs and costs. The sample omts two unverstes, Sunshne Coast and Notre Dame Australa, as both are relatvely small, and only began operaton n 2000. The Australan Natonal Unversty s ncluded, even though t had non-separable research fundng assocated wth the Insttute of Advanced Studes up to 1999: the data for the Australan Natonal Unversty accordngly only covers the perod snce 2000. The Australan Bureau of Statstcs consumer prce ndex (educaton) s used to convert all monetary varables from nomnal to real values (2000 = 100). The nputs and outputs employed follow a producton approach to modellng unversty behavour; that s, unverstes combne labour and non-labour factors of producton and produce outputs n the form of teachng, research, and research tranng. Sx categores of output are employed. These are the number of undergraduate, postgraduate, and PhD, the value of natonal compettve and ndustry grants (n $ thousands), and publcatons (n ponts). Note that student nclude degrees and other undergraduate qualfcatons whle publcatons nclude (ponts awarded n brackets) books (5 ponts), book chapters (excludng textbooks) (1 pont), refereed journal artcles (1 pont) and refereed conference proceedngs (1 pont) [see DEST (2006) for the elgblty crtera]. Unmstakably, the numbers of undergraduate and postgraduate awards are an obvous measure of output for any unversty. Smlarly, research s also an mportant output, sgnfed
9 by ongong government research fundng beng at the tme dstrbuted by a performance-based formula (weghtng n brackets) comprsng research ncome (60%), publcatons (10%) and doctoral students (30%). Nevertheless, there are three obvous lmtatons wth the selected output specfcaton. Frst, usng research ncome as a proxy for output s problematc n that t s arguably an nput nto the research process, not an output of the process. Ths could potentally nvolve msspecfcaton n that the output affects the level of nputs. However, the fact remans that n Australa the government and other unversty stakeholders regard research ncome as a key ndcator of unversty performance. Moreover, Flegg et al. (2004, p. 234) argue research ncome s lkely to reflect the perceved qualty, as well as quantty, of research output and t should provde a more up-to-date pcture of such output than, for example, publcatons or ctatons, for whch there s bound to be a consderable tme lag. Second, there s no drect allowance for qualty. Nevertheless, puttng asde the lack of alternatve measures, ths s entrely consstent wth current polcy n the sector. For example, Commonwealth fundng for students by dscplne s dentcal across unverstes, a dollar of compettve research ncome s treated the same regardless of ts source, and among the publcatons recognsed as research outputs, there s currently no attempt to dstngush between hgh and low-qualty outcomes. Ths was already lkely to change wth the prevous Lberal Natonal government s Research Qualty Framework (RQF) and now wth the current Labor government s stated objectve of promotng research qualty and evaluaton through the Excellence n Research for Australa (ERA) ntatve. Fnally, there s no recognton of the non-teachng and non-research outputs that unverstes can provde. These nclude nformed commentary by academcs n the meda and at publc forums and nqures, recreatonal servces lke sportng actvtes and cultural events, addtonal servces for ndgenous, rural, dsabled, and other dsadvantaged students and engagement wth busness and communty groups. In the absence of any specfc measurement, ths analyss assumes such unmeasured outputs ncrease n proporton to the measured outputs. The major costs n unversty teachng, research and research tranng are the salares of academc and non-academc staff. Unfortunately, the data do not allow the fner separaton of academc staff nto teachng-only, teachng and research, or research-only staff, nor s t possble to separate non-academc staff nto teachng or research-related support servces. Other nputs comprse non-labour expendture, and these typcally nclude the physcal support of academc actvtes and research, lbrares, other academc support servces, student
10 servces, publc servces, buldngs and grounds and admnstraton and other general nsttuton servces). In the past, a reasonable assumpton would be that the prces of all unversty nputs held constant across the sector, gven centralsed wage determnaton, the absence of enterprse barganng agreements, and so on. Increasngly, however, large dspartes have opened between unverstes n the prces of ther nputs, operatng as they do n an ncreasngly compettve market for academc labour (especally that ted closely to key research outcomes). One beneft of allowng prces to vary across unverstes s that t more accurately reflects dfferences n the relatve prces of nputs that may arse among unverstes operatng n dfferent envronments (ncludng captal cty vs. regonal unverstes, and unverstes n the varous states). Accordngly, the nput prce of academc (non-academc labour) for each unversty s determned by dvdng the expendture on academc (non-academc) salares by the number of full-tme equvalent academc (non-academc) staff. The prce of captal (non-labour nput) s proxed by dvdng non-labour expendtures by the stock of physcal captal. Unfortunately, unverstes do not provde ths nformaton to DEST and so a proxy s that unversty captal corresponds to the full-tme undergraduate and postgraduate student load. The total costs of each unversty each year are the sum of all labour and non-labour expendtures. Table 1 presents a summary of descrptve statstcs for annual costs, nput prces, and outputs for the 36 Australan unverstes from 1998 to 2006 (wth the excepton of the Australan Natonal Unversty (ANU), whch covers the perod 2000 to 2006). Sample means, medan, maxmums, mnmums and standard devatons are reported. Between 1998 and 2006, average annual total costs range from $88.1 mllon (Ballarat) to $783.3 mllon (Melbourne) wth a sector average of $301.4 mllon. The fve hghest cost unverstes comprse members of the Go8: namely, Melbourne ($783.3 mllon), Sydney ($752.3 mllon), Monash ($707.2 mllon), Queensland ($670.5 mllon), and New South Wales ($663.5 mllon). The sx lowest cost unverstes are Ballarat ($88.1 mllon), Charles Darwn ($88.5 mllon), Southern Cross ($88.8 mllon), Australan Catholc ($99.1 mllon), and Canberra ($108.5 mllon). < TABLE 1 HERE> In terms of nputs prces, the averages (n thousands) across the sector are $113.2 thousand for academc labour, $72.2 thousand for non-academc labour and $7.4 thousand for captal (the prces for labour are per equvalent full-tme staff member whle the captal
11 measure s per equvalent full-tme student). The lowest prced academc labour s at Southern Queensland ($87.1 thousand), New England ($94.8 thousand) and Charles Sturt ($95.7 thousand) whle the hghest prced academc labour s Swnburne ($161.8 thousand), Charles Darwn ($169.4 thousand) and Ballarat ($175.3 thousand). The lowest prced non-academc labour s at Southern Queensland ($57.3 thousand), New England ($59.6 thousand) and Edth Cowan ($60.4 thousand) whle the hghest prced s at Vctora Unversty of Technology ($86.5 thousand), Swnburne ($115.5 thousand) and Charles Darwn ($188.7 thousand). Fnally, the least cost captal s at Australan Catholc ($3.7 thousand), Charles Sturt ($4.1 thousand) and Southern Queensland ($4.3 thousand) whle the most costly captal s at Western Australa ($11.8 thousand), Charles Darwn ($12.9 thousand) and ANU ($25.1 thousand). The unverstes wth the hghest average undergraduate are Monash (8,454), Melbourne (7,242), Sydney (6,611), Queensland Unversty of Technology (6,006), Western Sydney (5,812) and the lowest are Charles Darwn (517), Ballarat (1,065), James Cook (1,600), Southern Cross (1,656) and Canberra (1,737). Across the sector, undergraduate average 3,573 students annually. For postgraduate, the sector average s 1,818 students wth New South Wales (3,964), Monash (3,893), Unversty of Technology Sydney (3,775), Melbourne (3,694), Sydney (3,127), graduatng more and Charles Darwn (309), James Cook (467), Tasmana (470), Murdoch (636), and Southern Cross (652) graduatng fewer postgraduate students. The fnal three outputs broadly correspond to unversty outputs n research and research tranng. The hghest number of doctoral s at Melbourne (444), Sydney (411), Queensland (380), New South Wales (338), Monash (309) and the lowest are at Unversty of Ballarat (12), Australan Catholc (16), Charles Darwn (17), Central Queensland (18) and Canberra (19). The sector average s 124 doctoral. For grants, Melbourne ($137.2 mllons), Sydney ($125.7 mllons), and Queensland ($106.3 mllons) rank hghest and the lowest s at Australan Catholc ($1.3 mllons), Ballarat ($1.8 mllons), and Central Queensland ($2.0 mllons). The overall annual average dollar value of natonal compettve and ndustry grants for perod s $28.2 mllon. Fnally, the average publcaton ponts per unversty per year s 937 wth the hghest average number of publcatons at Sydney (2,762), Queensland (2,712), and Melbourne (2,568), and the lowest average at Charles Darwn (123), Southern Cross (165) and Australan Catholc (186).
12 Model specfcaton A cost functon s employed to estmates the economes of scale and scope n Australan hgher educaton. The basc assumpton s that unverstes seek to mnmse ther costs at some chosen level of output subject to the relatve prces of ther factor nputs. Ths approach has been used n a relatvely large number of studes of hgher educaton costs n Australa and elsewhere [Cohn et al. (1989), de Groot et al. (1991), Lloyd et al. (1993), Lews and Dundar (1995), Hashmoto and Cohn (1997), Koshal and Koshal (1995; 1999; 2000), Izad et al. (2002), O Connell and Perkns (2003), Laband and Lentz (2003), Sav (2004), Stevens (2005), McMlland and Chan (2006), Lenton (2007) and Johnes et al. (2008)]. Alternatve approaches to the study of unversty costs nclude cost fronters [see Worthngton (2001) and Johnes (2006) for useful surveys of fronter effcency measurement n educaton]. A quadratc cost functon s used for ths purpose. Ths has the advantage of a flexble specfcaton applcable to multfactor producton. The cost functon s also an approprate form to take account of the lnear, quadratc and cross-product terms found wth more than one factor nput. A cost functon that allows the economes of scale to vary wth dfferent levels of nput prces and output s specfed as: 8 8 2 0 + β y + / 2 δ ( y ) = 1 = 1 8 C = β 1 + γ j y y j + ε (1), j j = 1 where β 0 s the fxed cost term, β ( = 1, 2,, 8) are the slope coeffcents of the lnear term, δ ( = 1, 2,, 8) are the slope coeffcents of the quadratc terms, γ j ( = 1, 2,, 8, j = 1, 2,, 8 and j) are the slope coeffcents of the cross-product terms, C s the of the total operatng costs of each unversty (n $ mllons) and y 1 to y 8 represent the prces of the academc and non-academc labour nputs and captal nputs (n $ thousands), undergraduate, postgraduate and PhD (n number), compettve grants (n $ thousands) and publcatons (n ponts). Usng Shephard s Lemma, the factor demands can be obtaned by dfferentatng the cost functon n equaton (1) wth respect to the nput prces. C P = C P P C = X C P = CS P ) ( (2) or
13 8 C CS( P ) = = β + δ y + γ j y j (3) P, j = 1 j where CS(P ) s the th factor cost share and X s the quantty of the th nput and P s the prce of the th nput (academc and non-academc labour and captal). It s possble to mprove the effcency of the parameter estmates by estmatng equaton (1) wth the cost share equatons (3). The cost share for the three nput prces must sum to one and ths restrcton produces sngularty n the covarance of equaton (3). The system of equatons s estmated jontly by omttng one of the cost share equatons n (3) together wth equaton (1) usng a seemngly unrelated regresson model mposng symmetry and the coeffcents of the three nput prce coeffcents to sum to one. The prce of captal s the omtted nput prce. The cost functon n (1) allows the estmaton of the economes of scale and scope. Followng Baumol et al. (1982), Cohn and Geske (1990), Lews and Dundar (1995) Hashmoto and Cohn (1997), Koshal and Koshal (1999; 2000), Sav (2004) and Johnes et al. (2008), these are defned as ray economes of scale, product-specfc economes of scale and product-specfc economes of scope. Under ray economes of scale, the composton of each unversty s output s assumed to reman fxed whle the aggregate sze of output vares. Ths provdes a measure of scale analogous to the sngle output case where ray economes (dseconomes) of scale exst f the measure s greater (less) than unty. Product specfc economes of scale, however, allow one output to vary, whle all other outputs are held constant. Product-specfc economes (dseconomes) of scale then exst f the measure s greater (less) than unty. Fnally, product-specfc economes of scope measure whether the cost of producng the outputs jontly s less than the costs of producng them separately. A value greater than or equal to zero thus ndcates that cost advantages accrue through the jont producton of outputs. The method for calculatng these measures s as follows. Frst, the average ncremental cost, AIC(y )) for producng output y s defned as: C( y) C( yn ) AIC( y ) = = 4, 5,...8 (4) y where C(y) s the total cost of producng the fve outputs and C(y N-1 ) s the total cost of producng zero unts of the th output. In the case of a sngle product, the economes of scale
14 are measured by the average ncremental cost dvded by the margnal cost. The productspecfc economes of scale for y, E(y ) are specfed as: AIC( y ) E ( y ) = (5) MC( y ) where MC y ) = C / y ) s the margnal cost of producng y unts of output. Ray economes ( of scale exst when the quanttes of the product are ncreased proportonately and are presented as: E( RAY ) = 8 = 4 C( y) y MC( y ) (6) If E(y ) or E(RAY) s greater than one (less) than one then economes of scale (dseconomes of scale) exsts for output y. Second, economes of scope can be dvded nto global economes of scope (GES) and product-specfc economes of scope (PES) and these are defned as: GES( y ) = 8 C( y ) C( y) = 4 C( y) (7) The product-specfc economes of scope are calculated as: C( y ) + C( yn ) C( y) PES( y ) = (8) C( y) Emprcal results The estmated coeffcents, standard errors and p-values of the cost functon are presented n Table 2. It s clear that the model wll nevtably have multcollnearty as the explanatory varables contan a lnear combnaton of nput prces and outputs together wth squared and cross-product terms. A smple test usng the parwse correlaton between the explanatory varables (not shown) ndcates the presence of collnearty wth 17 percent of the pars coeffcents exceedng the rule of thumb factor of 0.8. Accordngly, t s generally dffcult to nterpret the estmated slopes of quadratc cost functons. The R 2 for the cost functon n equaton (1) s 0.9862 and ths s comparable to smlar measures of predctablty n hgher educaton elsewhere. The null hypotheses of no nput prce or output effects are jontly tested n addton wth varous tests of no lnear, quadratc and output cross-product effects wth the
15 Ch-squared test statstcs n Table 2. All hypotheses are rejected at the one percent level of sgnfcance, thus suggestng that jontly all groups of explanatory varables should be ncluded n estmatng the cost functon for the thrty-sx Australan unverstes. < TABLE 2 HERE> The estmated quadratc cost functon n Table 2 s used to estmate the margnal costs (MC) and average ncremental costs (AIC) for each of the fve unversty outputs (undergraduate, postgraduate, PhD, natonal compettve and ndustry grants and publcatons) for levels of mean output runnng from 50% to 300% (.e. 100% s the mean output) n Table 3. The mean values are 3572.60 undergraduate, 1818.02 postgraduate and 123.54 PhD, $28155.99 (thousand) n natonal compettve and ndustry grants and 936.61 publcaton ponts. As shown, the margnal cost of undergraduate declnes over the varous levels of output, fallng from $49,962 per completon at 50% of mean output the $39,772 at 300% of output. However, the margnal costs of the remanng four outputs all ncrease as output ncreases from 50% to 300% of output, from just $4,711 to $50,464 per postgraduate completon, $129,839 to $512,362 per PhD completon, from $1.39 to $4.12 per dollar of natonal compettve and ndustry grants, and from $13,374 to $78,549 per publcaton pont. As n Lews and Dundar (1995), PhD are the most costly output at the margn for unverstes whle undergraduate are the least costly. < TABLE 3 HERE> However, whle the margnal costs ncrease prohbtvely at very hgh levels of output, the average costs are more stable. For example, at 200% of mean output, whle the average cost of an undergraduate completon s $47,924 compared to the margnal cost of $43,848, for postgraduate the average costs s just $9,795 compared to a margnal cost of $$30,192 and for PhD the average cost s $206,344 and the margnal cost s $359,353. Wth grants and publcatons the average (margnal) costs are $1.44 ($2.78) and $26,409 ($52,479), respectvely. Of course, ths s to be expected as changes n margnal costs take some tme to be reflected n sgnfcant changes n average costs. An mportant pont to note s that as the data avalable does not allow to be separated by dscplne, the margnal and average costs are across all dscplnes and we would expect substantally varaton n costs across, say, the socal, natural, mechancal and health scences.
16 The product-specfc and ray economes of scale are presented n Table 4. As defned earler, the pont estmates represent the degrees of ray economes (dseconomes) of scale: f the pont estmate s greater than unty, then ray economes of scale exst across the output set. As shown, ray economes (the proportonal augmentaton of output holdng composton constant) exst from 50% to 100% of the mean output over the sample perod. However, between 100% and 125% of mean output dseconomes arse and hold for all levels of mean output up to 300%. Ths suggests that the sector as a whole s currently experencng economes of scale and there s a clear ncentve to expand the producton of all outputs to explot exstng potental scale economes. However, dseconomes of scale wll arse f output ncreases beyond 125% of the mean. The fndngs also suggest that expandng output for smaller unverstes (less than 100% of the sector mean) would ncrease effcency n the producton of teachng, research and research tranng, assumng, of course, that the qualty levels of the outputs s held constant. < TABLE 4 HERE> Table 4 also ncludes the product-specfc economes of scale. Clearly, economes of scale for undergraduate are ncreasng for all tabled levels of output. However, postgraduate, PhD, natonal compettve and ndustry grants and publcatons there are dseconomes of scale at these levels of output and these appear relatvely stable. Ths complements the work of Lews and Dundar (1995) on Turksh unverstes who also found no evdence of scale economes n research output, and Koshal and Koshal (2000) who concluded declnng economes of scale n research and research tranng n US lberal arts colleges. However, t s mportant to note that dseconomes of scale can concde wth ncreasng returns to scale because ncreases n factor prces have offset any physcal gans. For nstance, the growth of the Australan unversty sector has seen ncreases n the factor prces for specalzed research and research tranng academc staff n a relatvely noncompettve ndustry and these may offset the benefts of scale. As wth most unversty systems, producton n Australan hgher educaton typcally nvolves jont producton as a teachng, research and research tranng outputs are produced jontly and t s not possble to dvde the costs of producton accurately nto ther separate uses. As shown n Table 4, the global economes of scope are postve and ncreasng for all levels of mean output. Ths ndcates that there are economes of scope at the exstng product combnaton and that these scope economes can be better exploted as scale ncreases. The
17 pattern of postve and ncreasng economes of scope s repeated for all of the productspecfc economes of scope wth the excepton of publcatons. These results suggest that materal opportuntes for the jont producton of undergraduate and postgraduate teachng and research tranng arse at all levels of output, but the evdence supportng scope economes n research s more mxed wth natonal compettve and ndustry grants beneftng from jont producton, but publcatons havng dseconomes of scope. Nevertheless, the dseconomes of scope for publcatons are declnng at very hgh levels of mean output (+300%) and may eventually become economes of scope; however, ths would be at a hgher level of output than any exstng Australan unversty. The fnal part of the analyss calculates a cost effcency ndex for ndvdual Australan unverstes over the sample perod by comparng ther predcted costs usng the sector wde equaton n Table 2 and ther own combnaton of factor nput prces and levels of outputs and ther actual mean costs over the perod. In ths table, a cost effcency value greater (less) than unty ndcates that actual costs are hgher (lower) than the theoretcal costs. That s, the unversty s cost neffcent (effcent) n terms of the sector benchmark f the ndex value s less (greater) than unty. It s also mportant to note that cost effcency ncludes both techncal effcency the ablty to maxmze outputs relatve to a gven level of nputs, or equvalently, mnmze nputs for a gven level of output and allocatve effcency---the ablty to employ factor nputs n ther optmal proportons gven ther respectve prces. We leave the decomposton of cost effcency nto ts techncal and allocatve components for future study. As shown, there appears to be no clear connecton between the measure of cost effcency and membershp of one of the unversty lobby groups that have arsen n recent years (Group of Eght, Innovatve Research Unverstes Australa, Australan Technology Network, New Generaton Unverstes and ungrouped unverstes). However, at least some of these unverstes have been the subject of recent publcty n terms of a deteroratng and/or challengng fnancal poston. For example, Central Queensland, Queensland Unversty of Technology, Grffth Unversty and the Unversty of Queensland are hgh-cost mult-campus unverstes based n Queensland that have grown substantally n recent years (the Queensland Unversty of Technology closed ts Carseldne campus n 2008). Smlarly, La Trobe s usng staff cuts to restore ts operatng surplus to 3 per cent of revenue n 2009 (Trounson 2008); Royal Melbourne Insttute of Technology has been the subject of serous ongong fnancal management problems, ncludng budget blowouts and poor busness
18 plannng; whle James Cook recently expressed concern about meetng staff demands for pay and condtons n the next enterprse barganng agreement. Concludng remarks Ths study examned economes of scale and scope n Australan unverstes over the perod 1998 to 2006. The nputs ncluded n the analyss are full-tme equvalent academc and nonacademc staff and non-labour expendture and the outputs are undergraduate, postgraduate and PhD, natonal compettve and ndustry grants and publcatons. Productspecfc and ray economes of scale and product-specfc and global economes of scope are calculated usng estmates from a quadratc cost functon. The man fndngs are as follows. Frst, there s evdence of ray economes of scale (assumng the composton of outputs remans unchanged) but only up to 100% of mean output. After ths pont, dseconomes of scale arse and so there s lttle ncentve for unverstes to expand output far beyond current levels, at least n terms of ray economes of scale. However, there are contnuous ncreases n product-specfc economes of scale for undergraduate, from 50% to 300% of the mean output, and ths suggests further ncreases n output n ths area could be at lower average cost. Second, n contrast the evdence for economes for scope s very strong, wth global economes of scale at all levels of mean output. Ths ndcates that unverstes beneft (n terms of cost) from the jont producton of teachng, research, and research tranng outputs. However, whle product-specfc economes of scope hold for undergraduate, postgraduate and PhD and grants, there are dseconomes of scope when publcatons ncrease relatve to the other outputs. Ths suggests there s a cost dsadvantage assocated wth the producton of publcatons n solaton from other unversty outputs. In terms of future research, a key lmtaton of ths analyss s that no drect allowance has been gven to the qualty of nputs and outputs. For example, f the qualty of outputs ncreases substantally wth output, the dseconomes found wth the quantty only output of publcatons may convert to economes of scale. From a dfferent perspectve, t s also unlkely that the academc nputs across the sector are consstently of the same qualty. Possble extensons to address the former would be to nclude the Academc Rankng of World Unverstes compled by Shangha Jao Tong Unversty (regretfully only avalable snce 2003) for a unversty-wde measure of qualty or the Graduate Careers Australa's annual Australan Graduate Survey for teachng outputs only. Clearly, the current emphass of
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