The purpose of this paper is to provide an in-depth study of the cost structure and efficiency of English higher education institutions (HEIs). We are particularly interested, given the change in the composition of the sector, in how costs structures and efficiency vary by mission group. Previous work has focussed on pre-determined mission groups; but that is not necessarily satisfactory as mission groups were often formed historically, and universities which may once have had similar missions may not necessarily have similar outlooks today. To this end we use a panel of data from the English higher education sector

from 2002/03 to 2010/11 to estimate a cost function for English HEIs using the latent class

variant of the stochastic frontier model. This allows us simultaneously to (i) identify clusters

of institutions, based on what the data tell us, (ii) evaluate the parameters of the cost

function for each cluster, thence evaluating also measures of economies of scope and of scale

within each cluster, and (iii) measure the efficiency of each institution, both relative to other institutions in the same cluster and relative to all other institutions in the analysis

Johnes, Geraint

Johnes, Jill

English

University of Huddersfield Repository

University of Huddersfield RepositoryJohnes, Jill and Johnes, GeraintCosts and efficiency in English higher education: An analysis using latent class stochastic frontier modelsOriginal CitationJohnes, Jill and Johnes, Geraint (2015) Costs and efficiency in English higher education: An analysis using latent class stochastic frontier models. In: 5th Workshop on Efficiency and Productivity Analysis, 5 October 2015, Catholic University Porto, Portugal. (Unpublished) This version is available at http://eprints.hud.ac.uk/27830/The University Repository is a digital collection of the research output of theUniversity, available on Open Access. Copyright and Moral Rights for the itemson this site are retained by the individual author and/or other copyright owners.Users may access full items free of charge; copies of full text items generallycan be reproduced, displayed or performed and given to third parties in anyformat or medium for personal research or study, educational or not-for-profitpurposes without prior permission or charge, provided:• The authors, title and full bibliographic details is credited in any copy;• A hyperlink and/or URL is included for the original metadata page; and• The content is not changed in any way.For more information, including our policy and submission procedure, pleasecontact the Repository Team at: E.mailbox@hud.ac.uk.http://eprints.hud.ac.uk/COSTS AND EFFICIENCY  IN ENGLISH HIGHER  EDUCATION 5th Workshop on Efficiency and Productivity Analysis  Porto 5th October 2015   Jill Johnes, University of Huddersfield UK Geraint Johnes, Lancaster University UK AN ANALYSIS USING LATENT CLASS  STOCHASTIC FRONTIER MODELS Outline of talk   1. Introduction  2. Literature review 3. Conceptual issues 4. Model specification - Defining the variables - Estimation method 5.  Results - Estimated average costs - Economies of scale - Economies of scope - Efficiencies 6. Conclusions https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/237411/bis-13-918-efficiency-in-higher-education-sector.pdf    1. Introduction • HEIs receive public money - funding body grants - non-payment of tuition fees • Reduced incentive to be efficient • Need to assess efficiency of higher education institutions (HEIs)  18% 47% 16% 18% 1% Sources of university incme in England 2013/14 Funding body grantsTuition fees andeducation contractsResearch grants andcontractsOther incomeEndowment andinvestment income• Cost functions provide information on efficiency, economies of scale and economies of scope 1. Introduction The English higher education sector comprises very diverse groups of HEIs:   Pre-1992 universities: degree programmes in all academic subjects; research mission  Post-1992 universities: degree programmes in academic and vocational subjects; some have a research mission  Former colleges of HE: small, specialist HEIs; most do not have a research mission  1. Introduction Questions • What are average and marginal costs of outputs of English HEIs? • Are there economies of scale and scope in English HE? • How efficient are English HEIs? • How does ‘mission group’ affect costs? • Are there other factors which might affect HEIs’ costs?  2. Literature Review • USA: Cohn et al (1989) • UK: Glass et al (1995a; 1995b); Johnes (1996; 1997; 1998); Izadi et al (2002); Stevens (2005); Johnes et al (2005; 2008); Thanassoulis et al (2011)    Allow for economies of scale and scope  Disaggregate output by subject and by type of HEI  Limited analysis of additional variables   Increasing use of panel data   Generally cover a subset of the English HE sector 2. Literature Review • USA: Cohn et al (1989) • UK: Glass et al (1995a; 1995b); Johnes (1996; 1997; 1998); Izadi et al (2002); Stevens (2005); Johnes et al (2005; 2008); Thanassoulis et al (2011)    Relatively low efficiency in panel data studies   Efficiency varies by type of university  Ray economies of scale; diseconomies of scope  Student quality, location of HEI are not important determinants of costs   2. Literature Review Most recent developments • UK: Johnes & Johnes (2009) use a random parameter model (RPM) with stochastic frontier analysis (SFA)  Allows HEIs to have different objectives; the model allows the coefficient on one output to vary by HEI   Can be difficult to estimate the parameters of a RPM SFA • Findings:  HEIs are heterogeneous in terms of both cost structure and efficiency 2. Literature Review Most recent developments • USA: Agasisti & Johnes (2009) use latent class model (LCM) with SFA  Rather than calculating cost functions by pre-defined groups, they use the LCM method to let the data suggest distinct groups • Findings:  HEIs are heterogeneous in terms of both cost structure and efficiency 3. Conceptual Issues Functional form of cost function a) Linear: � = ࢻ૙ +  ࢼ࢏�࢏࢏  b) CES: � = ࢻ૙ +  ࢼ࢏�࢏ࢾ࢏࢏ � + � c) Quadratic: � = ࢻ૙ + �࢏�࢏ +  ࢼ࢏�࢏ + ૚૛   ࢽ࢏࢐�࢏�࢐࢐ + �࢏࢏࢏  d) Hybrid translog:  3. Conceptual Issues • Average incremental cost (AIC) ��� �� = � � − � ��−� /�� • Ray economies of scale   �� = � � ���� ��  where �� � = �� ���� = ���  If SR > 1 (< 1) then there are economies (diseconomies) of scale Note that � �  is the total cost of producing all N outputs.    3. Conceptual Issues • Product-specific economies of scale  �� � = ���ሺ��ሻ/��ሺ�ሻ      If Si > 1 (< 1) then there are economies (diseconomies) of scale for product i • Economies of scope   �� =  � �� − � �� /�ሺ�ሻ   If SG > 0 (< 0) then global economies (diseconomies) of scope exist for producing the outputs jointly rather than in separate institutions    4. Model Specification a) Outputs TEACHING • UGMED FTE undergraduates in medicine and dentistry (000s) • UGSCI FTE undergraduates in sciences other than medicine and dentistry (000s) • UGARTS FTE undergraduates in non-science subjects (000s) • PG FTE postgraduates in all subjects (000s) 4. Model Specification a) Outputs RESEARCH • RESEARCH Quality related funding and research grants THIRD MISSION • IPINCOME Income from third mission activity Note that all squares and interactions of UGMED, UGSCI, UGARTS, PG and RESEARCH are included; the square of IPINCOME and interaction of IPINCOME only with RESEARCH are included.    4. Model Specification b) Additional factors QUALITY OF STUDENTS • MEANSAL Mean salary of graduates 6 months after graduation QUALITY OF TEACHING • NSS Percentage saying yes to the question: ‘Overall, I am satisfied with the quality of the course’ from the National Student Survey  4. Model Specification b) Additional factors WIDENING PARTICIPATION • LOWPNO Number of FT UG entrants from ‘low participation’ neighbourhoods ESTATES COSTS • LISTED The total area of the HEI identified as a listed building   4. Model Specification b) Additional factors DUMMY VARIABLES • OXBRIDGE Dummy variable: 1 if HEI is Oxford or Cambridge • YEAR Dummy for each year in the study (apart from the last)   4. Model Specification c) Estimation  • SFA  For HEI i at time t: ��� = � �1�� , … , ���� + ݒ�� + ݑ��   • SFA with latent class model (LCM)  For HEI i at time t, m classes: ��� = �� �1�� , … , ���� + ݒ��,� + ݑ��,�      5. Results • Panel data from 2003/04 to 2010/11 covering around 120 HEIs • Model estimates for 3 time periods: 2003/04 to 2004/05, 2005/06 to 2007/08 and 2008/09 to 2010/11  • Comparison of results from applying SFA and SFA LCM  • Efficiency is allowed to vary over time within any given model • Data are largely from the Higher Education Statistics Agency • All money units are in 2011 values 5. Results AIC from SFA linear model (2011 £)      Other outputs included: RESEARCH, IPINCOME Controls for: LISTED, LOWPNO, YEAR dummies, OXBRIDGE AICs 2008/09 to 2010/11 2005/06 to 2007/08 2003/04 to 2004/05 UGMED 13484 13866 9748 UGSCI 7775 7040 5609 UGARTS 4574 6657 3951 PG 13953 9409 9818 5. Results AIC from the linear SFA LCM (2011 £)       Other outputs included: RESEARCH, IPINCOME Controls for: LISTED, LOWPNO, YEAR dummies, OXBRIDGE      2008/09 to 2010/11 2005/06 to 2007/08 2003/04 to 2004/05 AICs Class 1 Class 2 Class 1 Class 2 Class 1 Class 2 UGMED 10865 7774 9732 6623 2406 9446 UGSCI 1931 8472 1748 8641 2538 7055 UGARTS 9353 2757 8166 4659 6502 4427 PG 246 18694 10459 5754 13432 8614 No. in each class 121 234 111 216 60 136 5. Results Histogram of efficiency scores Final year of linear 2008/09 to 2010/11 model   051015202530354045-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency 5. Results Histogram of efficiency scores Final year of 2008/09 to 2010/11 linear latent class model  Latent class 1   Latent class 2       02468101214-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Frequency 05101520253035-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Frequency 5. Results Akaike Information Criterion (AkIC) AkIC = -2.logLF(m) + 2.k  where k is the number of estimated parameters    No. of classes 2008/09 to 2010/11 2005/06 to 2007/08 2003/04 to 2004/05 1 8393.3 7574.0 4356.5 2 7711.9 7019.1 4119.4 3 7637.9 6989.6 4081.7 4 7561.9 6921.7 4037.7 5. Results AIC from SFA quadratic model (2011 £)       Other outputs included: RESEARCH, IPINCOME Controls for: LISTED, LOWPNO, YEAR dummies, OXBRIDGE     AICs 2008/09 to 2010/11 2005/06 to 2007/08 2003/04 to 2004/05 UGMED 16034 15000 9195 UGSCI 7858 9444 4591 UGARTS 5459 4587 329 PG 5275 2601 7073 5. Results AIC from quadratic SFA LCM (2011 £)        Other outputs included: RESEARCH, IPINCOME Controls for: LISTED, LOWPNO, YEAR dummies, OXBRIDGE     2008/09 to 2010/11 2005/06 to 2007/08 2003/04 to 2004/05 AICs Class 1 Class 2 Class 1 Class 2 Class 1 Class 2 UGMED 8720 19595 8351 8933 3958 4962 UGSCI 5260 7185 7708 11109 860 8753 UGARTS 5883 2176 -2354 6146 764 6576 PG 7839 1242 -10071 306 -4895 376 No in each class 236 119 132 195 100 96 5. Results Economies of scale Quadratic model (for a HEI with mean levels of output) 2008/09 to 2010/11           SFA SFA class 1 SFA class2 Ray economies 1.01 0.95 0.97 UGMED 1.25 1.11 1.23 UGSCI 1.00 1.26 0.75 UGARTS 1.23 0.84 0.46 PG 0.78 0.60 0.25 RESEARCH 1.13 0.97 1.00 IPINCOME 1.09 1.12 1.00 5. Results Economies of scope Economies of scope (for a HEI with mean levels of output)     SFA SFA class 1 SFA class2 Global economies -0.01 -0.13 -0.01 5. Results Histogram of efficiency scores – final year of 2008/09 to 2010/11 quadratic model  05101520253035404550-1 -0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Frequency 5. Results Histogram of efficiencies – final year of 2008/09 to 2010/11 quadratic latent class model  Latent class 1   Latent class 2        05101520253035-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Frequency 051015202530-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Frequency 5. Results Comparison of Models with Akaike Information Criterion (AkIC) AkIC = -2.logLF(m) + 2.k  where k is the number of estimated parameters    No. of classes 2008/09 to 2010/11 2005/06 to 2007/08 2003/04 to 2004/05 1 -661.0 -367.7 -326.4 2 -848.9 -770.0 -567.8 3 -915.9 -922.8 -579.4 5. Results Pre-defined classes    2008/09 to 2010/11  AICs  Specialist High tariff Medium tariff Low tariff UGMED 12178 8265 8414 8839 UGSCI 2080 9827 8085 5024 UGARTS 12263 14850 3227 6925 PG 6411 11358 14609 11087 No. in each class 111 84 96 87 Is λ significantly different from zero at the 5% significance level? YES NO NO YES 6. Conclusions • Results for the earliest time period seem unreliable • Estimates of AICs from SFA models (linear and quadratic) for the remaining periods seem plausible • Estimates of AICs from SFA LCM seem less precise • Ray economies of scale are exhausted; there are product specific economies in UG teaching and in research • There are diseconomies of scope 6. Conclusions • It is important to take into account other characteristics of universities (observable and unobservable) in estimating cost functions – efficiency differences are much lower once this is done • Where a HEI has a low efficiency score this is usually explained by reference to special features observed in that HEI (eg. small, specialist) • Can the LCM adequately deal with the heterogeneity observed in English higher education? 

Costs and efficiency in English higher education: An analysis using latent class stochastic frontier models

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