Using Data Envelopment Analysis to Improve Estimates of Higher Education Institution’s Per‐student Education Costs¹

1. An earlier draft of this paper was presented in September 2003 at the 16th Annual Consortium of Higher Education Researchers Conference in Porto, Portugal.

Abstract

This paper puts forth a data envelopment analysis (DEA) approach to estimating higher education institutions’ per‐student education costs (PSCs) in an effort to redress a number of methodological problems endemic to such estimations, particularly the allocation of shared expenditures between education and other institutional activities. An example is given using data for a sample of higher education institutions in The Netherlands and the results are compared with PSC estimates generated by a more traditional approach. Although several methodological concerns still persist, the use of DEA is argued to increase the likelihood of producing more realistic cost estimates for individual institutions.

Key Words:

• Higher education
• resource use
• costs
• efficiency
• data envelopment analysis

Acknowledgements

The author would particularly like to thank Ben Jongbloed and the two anonymous referees for their very useful comments. As usual, all mistakes and omissions are purely the author’s own. This research was supported by the Netherlands Ministry of Education, Culture and Science (Nederlands Ministerie van Onderwijs, Cultuur en Wetenschappen).

Notes

1. An earlier draft of this paper was presented in September 2003 at the 16th Annual Consortium of Higher Education Researchers Conference in Porto, Portugal.

2. The most common alternative is to estimate the marginal or incremental cost incurred from enrolling an additional student or producing an additional unit of research. Although such measures are particularly useful for exploring the extent to which IHEs can realize economies of scale and scope, we restrict ourselves here to the body of research focusing on average total cost estimation.

3. Institutions’ undergraduate populations are, in practically all cases, much larger than their graduate student populations. At the same time, it may be the case that laboratory equipment and other capital purchased initially for research activities through project funding may well be used in undergraduate laboratories at a later date.

4. Note also that the model here assumes that the production frontier can be characterized by constant returns to scale. This implies that if some input/output combination is feasible then, for any positive scalar, the larger input/output combination is also feasible.

5. Efficiency maximization does not imply that best‐performing institutions are fully efficient, hence it is not possible to state that they are operating at minimum cost. Moreover, only a select number of decision‐making units (DMUs) in a DEA analysis will ever be found to be relatively efficient. What the earlier statement means is that since inefficiency can already be seen as a penalty for an institution in a given analysis, let us attempt to minimize that penalty as much as possible.

6. Even where two institutions get projected back to the same facet of the efficient frontier, the weights will still differ unless the two institutions use exactly the same input proportions (i.e., one institution is a scaled down or up version of the other).

7. The more general formulation of the shared resources model takes into account that some inputs can only be used for certain activities (see Mar‐Molinero, 1996). While this may be a more realistic reflection of the input/output relationships in higher education institutions, the focus here is on allocating ‘reported’ expenditures data, which implies that the simplifying assumption can be safely imposed.

8. The mathematical explanation for how the resource allocation decision is made is beyond the scope of this paper and the reader is referred to Mar‐Molinero (1996) for a detailed explanation. Briefly, however, this is done to ensure that q takes the same value when computed by either the primal or dual linear program.

9. These groupings were produced by first sorting on the basis of whether each institution’s education offerings could be grouped into a single cluster of like programs or whether it had a broad array of multi‐cluster offerings. This gave rise to the following categories of institutions: (1) laboratory‐based (e.g., technology); (2) teacher training and social science institutes; (3) multi‐disciplinary; (4) multi‐disciplinary but without medical related programs; and (5) multi‐disciplinary without medical and performance arts programs.

10. Contract‐based funding, or third stream funding as it is commonly referred to, includes revenues for research activities but also for contracted education services as well.

11. Although there is no fixed decision rule for the minimum number of decision‐making units in an analysis, a good rule of thumb is that the number should equal or exceed three times the product of the inputs and outputs specified (Cooper et al., 2000). As was explained to me by Mar‐Molinero, one particularly appealing characteristic of the shared resources model is that the minimum number of DMUs is less than that required by the more general DEA models. This can be seen in equations (6) and (7). Although two inputs and two outputs are employed, the shared resources model simultaneously estimates two models (one for each output) not one. This means that for each case here there is one output and two inputs. Using the rule of thumb above, the minimum number of institutions is 3 × (2 × 1) = 6.

12. As can be seen in the tables, two‐thirds of the DEA estimates were lower than traditional ones and one‐third were higher.

13. These two results illustrate the point but are considerably extreme when compared with all of the other estimates in our study. This may suggest that there are unobserved problems with the underlying data for these two particular institutions.