Stochastic frontier estimation of a CES cost function: the case of higher education in Britain

Abstract Many estimates exist in the literature of multi-product cost functions estimated across a sample of institutions of higher education. Typically these have not employed the appropriate frontier estimation techniques. The cost functions usually estimated — such as the constant elasticity of substitution (CES) function — are highly non-linear, and the standard software packages do not allow stochastic frontier estimation in such cases. We derive and maximise the likelihood function associated with this problem, and hence construct measures of economies of scale and scope which obtain in British higher education. We use the half-normal residuals generated by the stochastic frontier estimation to construct measures of technical efficiency for each university in our sample.

[1]  G. Johnes.  Corrigendum: Costs and Industrial Structure in Contemporary British Higher Education , 1998 .

[2]  C. Lovell,et al.  On the estimation of technical inefficiency in the stochastic frontier production function model , 1982 .

[3]  D. Breneman,et al.  The costs of higher education , 1980 .

[4]  Ross Williams,et al.  Amalgamations of universities:are there economics of scale or scope? , 1993 .

[5]  R. Brent.  Table errata: Algorithms for minimization without derivatives (Prentice-Hall, Englewood Cliffs, N. J., 1973) , 1975 .

[6]  D. Aigner,et al.  P. Schmidt, 1977,?Formulation and estimation of stochastic frontier production function models,? , 1977 .

[7]  Noel Hyndman,et al.  The achievement of scale efficiency in UK universities: A multiple-input multiple-output analysis , 1995 .

[8]  Halil Dundar,et al.  Departmental Productivity in American Universities: Economies of Scale and Scope , 1995 .

[9]  C. G. Broyden.  The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations , 1970 .

[10]  E. Cohn,et al.  Economies of Scale and Scope in Japanese Private Universities , 1997 .

[11]  W. Baumol,et al.  Contestable Markets and the Theory of Industry Structure , 1982 .

[12]  E. Cohn,et al.  Institutions of Higher Education as Multi-product Firms: Economies of Scale and Scope , 1989 .

[13]  G. Johnes.  COSTS AND INDUSTRIAL STRUCTURE IN CONTEMPORARY BRITISH HIGHER EDUCATION , 1997 .

[14]  C. G. Broyden.  The Convergence of a Class of Double-rank Minimization Algorithms 2. The New Algorithm , 1970 .

[15]  R. Ball,et al.  Performance indicators in higher education , 1987 .

[16]  Antreas D. Athanassopoulos,et al.  Assessing the Comparative Efficiency of Higher Education Institutions in the UK by the Means of Data Envelopment Analysis , 1997 .

[17]  G. Johnes.  The British Experience of Reform in Education. , 1996 .

[18]  J. Fredericks Volkwein,et al.  The Cost Structure of American Research Universities , 1991 .

[19]  C. Propper,et al.  Quasi-Markets in the Welfare State , 1994 .

[20]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[21]  Noel Hyndman,et al.  Efficiency in the provision of university teaching and research: An empirical analysis of UK universities , 1995 .

[22]  G. Johnes.  The Management of Universities: President's Lecture Delivered at Annual General Meeting of the Scottish Economic Society 6-8th April 1999 , 1999 .

[23]  R. Nelson,et al.  Effect of class size on economies of scale and marginal costs in higher education , 1992 .

[24]  T. Coelli.  Estimators and hypothesis tests for a stochastic frontier function: A Monte Carlo analysis , 1995 .

[25]  G. Johnes.  Multi-product cost functions and the funding of tuition in UK universities , 1996 .

[26]  D. R. Lewis,et al.  Economies of Scale and Scope in Turkish Universities , 1995 .