Higher education institutions’ costs and efficiency: Taking the decomposition a further step

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Abstract

A multiproduct cost function is estimated for English higher education institutions using a panel of data from recent years. The panel approach allows estimation by means of a random parameter stochastic frontier model which provides considerable new insights in that it allows the impact on costs of inter-institutional differences in the cost function itself to be distinguished from inter-institutional differences in efficiency. The approach used here therefore resembles in some respects the non-parametric methods of efficiency evaluation. We report also on measures of average incremental cost of provision and on returns to scale and scope.

Introduction

The evaluation of costs in higher education has long been of interest to students of education economics. Theoretical insights into the operation of multiproduct organisations by Baumol, Panzar, and Willig (1982) rapidly led to the empirical evaluation of sophisticated cost functions in the sphere of higher education (Cohn, Rhine, & Santos, 1989). Later contributions refined the analysis by using frontier estimation methods that simultaneously evaluate cost structures and the technical efficiency of institutions (Johnes, 1996).1 In these papers a parametric cost function is estimated which is assumed to be stable across institutions that are heterogeneous in terms of their efficiency. The present paper takes the analysis a step further by estimating costs in a framework that allows institutions to differ in terms of both their efficiencies and their cost technologies.

Research on efficiency measurement has, since the seminal work of Farrell (1957) bifurcated, with economists typically following the route of statistical analysis (Aigner, Lovell, & Schmidt, 1977) and management scientists characteristically opting for a non-parametric route grounded in linear programming (Charnes, Cooper, & Rhodes, 1978). The former approach has come to be known as stochastic frontier analysis, the latter as data envelopment analysis (DEA). The relative merits and demerits of the two approaches are by now well known: the parametric statistical approach benefits from the availability of the toolkit of statistical inference, but imposes a common functional form and common parameters on all decision-making units; the alternative non-parametric approach is attractive in that it does not impose a common loss function on all units, but it lacks a statistical apparatus and its results may be sensitive to the presence of outliers.

Recent developments in the analysis of panel data have made available a new approach which combines the merits of both the statistical and non-parametric methodologies while suffering from none of the drawbacks. Tsionas (2002) and Greene (2005) have developed random parameter formulations of the stochastic frontier model which (in common with DEA) allow a separate loss function to be estimated for each decision-making unit while (in common with traditional frontier models) retaining the apparatus of statistical inference. In essence these models are simply a generalisation of the random effects frontier model introduced by Battese and Coelli (1995); while the random effects model allows only the constant to vary across decision-making units, however, the random parameters model allows any number of the other coefficients to vary as well. A distinction between these models and DEA is that the cross-unit variation is constrained to follow a specified statistical distribution; this constraint allows us to retain the toolkit of statistical inference.

In the context of higher education institutions, the development of this new methodology is particularly significant. It is well understood that HEIs do not represent an homogenous group. Some are old, some are new, some are big, some are small, some focus on certain subject groups, others focus on others, some are comprehensive in their provision, others are more specialised, some are research intensive, others not, and so on. Early studies of cost functions for UK institutions (such as Glass et al., 1995a, Glass et al., 1995b) focused purely on traditional universities. Later studies (for example, Johnes, 1997) looked at all universities, but excluded other providers of higher education such as colleges. The most recent work (Johnes, Johnes, Thanassoulis, Lenton, & Emrouznejad, 2005) includes higher education colleges as well as universities, but devotes much space to the separate estimation of cost functions specific to certain pre-specified groups of institutions. This approach is far from ideal, however, because the distinctions between traditional universities, former polytechnics, and colleges of higher education have become increasingly blurred over time. An alternative approach, and the one on which the present paper is founded, is to develop an integrated framework for the estimation of costs, but to let the data decide the parameters of the cost function that apply uniquely to each institution.

To motivate the analysis a little further, consider a comparison between four institutions. One is an ancient university, where learning is delivered primarily through small group tutorials. This university has high costs because the student:staff ratio is necessarily low. But it delivers learning in a form that might be deemed desirable, albeit not one that would be cost-effective if applied to the mass of higher education institutions.2 The second institution might also have high costs, but in this case they are due to locational factors; perhaps the institution is located in the nation's capital, where space and other costs are relatively high. The third institution has relatively high costs because (within the subject mix categories used in the analysis) it teaches expensive subjects; for instance, medicine may be more costly to deliver than other science subjects, but our analysis fails to disaggregate subjects sufficiently to identify medicine as a separate output. The fourth institution has moderate costs, as it does not have an adverse location or a need to employ unusually expensive teaching technologies. Now in a simple cross-section frontier analysis, the first three institutions may appear to be inefficient because of their high costs. In fact, however, there are reasonable explanations for these high costs, and these should not necessarily be put down to inefficiency. It is clear, therefore, that it is desirable that we should establish a method whereby unobserved heterogeneity in the cost function across institutions, on the one hand, and inefficiency, on the other, can be disentangled. That is the aim of this paper.

We employ recent developments in order to analyse the cost function for each higher education institution in England. Both random effects and more general random parameters models are estimated using panel data for 3 years, 2000–2001 through 2002–2003. Hence differences in intercept and slope coefficients across institutions can be estimated alongside differences in institutions’ efficiency. The next section discusses the data. Results and analysis are provided in the following section. The paper ends with a conclusion and suggestions for further research.

Section snippets

Data

Our data are drawn from English institutions of higher education over a 3-year period from 2000–2001 through 2002–2003. Some 121 institutions are included in the analysis; this includes ancient universities (such as Oxford and Cambridge), traditional universities (comprising all those institutions with university status prior to 1992), new universities (granted university status in or since 1992), and Colleges of Higher Education.3

Methodology and results

Cost functions in economic theory represent an envelope or boundary which describes the lowest cost at which it is possible to produce a given vector of outputs. As it is an envelope that we wish to model, it is necessary to employ frontier methods of estimation rather than the more conventional best fit technology.

The conventional approach to stochastic frontier estimation, based upon cross-section data, is due to Aigner et al. (1977). In this model, the equationyi=α+βxi+vi±uiis estimated

Conclusions

Earlier studies which have estimated cost functions for institutions of higher education have failed to recognise that, owing to unobserved heterogeneity, each institution likely faces a different cost function. In this paper, we use methods that have recently become available to estimate frontier cost functions for higher education institutions within the context of a random parameter model. This brings the analysis somewhat closer to the spirit of non-parametric techniques such as DEA (and

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