The DEA methodology was developed for estimating efficiency in the outputs and inputs of not-for-profit entities (Charnes et al. 1978). Since these organizations do not follow general
behavioral assumptions like profit maximization or cost minimization, the standard efficiency techniques are not useful. DEA is useful in situations when efficiency cannot be estimated with direct market results, i.e. profitability. The technique was inspired by the work of Farrell (1957), but the real impetus for using DEA in the efficiency studies came from Charnes et al. (1978). Since then the method has been used in different settings and it has been further advanced to incorporate variable return to scale, panel data and other specificities.
DEA is a non-parametric programming technique to measure the efficiency of one organization relative to other similar organizations. The technique constructs a technology frontier- i.e. the maximum output that can be produced with given inputs or outputs. The frontier is constructed entirely from empirical data, without any assumptions about the production process or behavior. The general logic of the method is illustrated in Figure 6.5.
Figure 6.5 Diagrammatic representation of an output-oriented DEA
Figure 6.6 Efficiency, technology and productivity changes
Adapted from Coelli et al. (2005) and Johnes (2006) Adapted from Coelli et al. (2005); Worthington & Lee (2005)
The technique defines efficiency as a ratio of weighted outputs to weighted inputs and the weight structure is calculated by mathematical programming. The organization on the frontier (A, B, or C) is defined as fully efficient and get a score of 1. Other organizations (E) get an efficiency
et al. (1995) present further details. For the empirical estimation in this study, the program by Coelli et al. (2005) has been used.
DEA also gives an insight in the source of inefficiency. Technical efficiency demonstrates the extent to which the organization is successful in maximizing output from existing inputs. Allocative efficiency measures the extent to which inputs are used in optimal proportions. Allocative efficiency is rarely examined in the higher education sector because the optimal balance between inputs depends on their relative price, but input prices are often not easily available in the sector.
Scale efficiency is another form of potential efficiency. Universities may be technically efficient but they may provide too much or too little output for maximum efficiency. On the other hand, universities are often not flexible in adjusting the scale. The size of the university is to a large extent under the control of the central administration that makes decisions about the number of publicly funded students and allocates institutional grants. Therefore, the DEA model must allow varying rates of return for meaningful results. On the other hand, information on scale efficiency may give valuable insights about the potential efficiency loss because of sub-optimal distribution of resources between universities.
The Malmquist index has been adapted for the panel data and it allows the DEA to explore productivity change more specifically. The Malmquist index decomposes changes in the technical efficiency into two parts: pure technical efficiency and technological change. This means that the productivity change over time may be explained either by the movement relative to the frontier, or by the shift of the frontier itself. The idea is illustrated in Figure 6.6. The frontier F represents the efficient level of output (y) that can be produced from a given level of input (x). The frontier may shift in time (from Ft to Ft1), which indicates technological change. When a university operates in point zt (using inputs of xt and producing ytoutputs), the university operates below the production frontier. With the available technology it could produce
outputs at the levelya. In the next period the university shifts to the point zt1, which is again
inefficient, but with respect to the new higher production frontier. The Malmquist index attempts to decompose the change in the output/input ratio into two components: technical efficiency change (moving closer to the frontier) and technological change (the shift of the frontier). Technical efficiency change is further decomposed into scale efficiency change and pure technical change.
While DEA has proven to be a helpful tool in the economics of higher education, the technique has limitations. Most importantly, the measure only captures relative efficiency. The best performing organizations are assumed to be fully efficient and are assigned the maximum score of 1. The efficiency of other organization is measured relative to the best performing organizations. The measure, however, does not say how efficient the best performing organizations actually are. The final result would demonstrate high average efficiency when all organizations are performing relatively poorly, but are homogenous in their poor performance. Secondly, there is no test of statistical significance of efficiency scores and inferences are based on geometrical averages.
Finally, the quality of the DEA results depends on the quality of data. The model requires that all relevant outputs and inputs are specified. Often, however, all output variables (or input variables) are not easily measurable. Furthermore, even when the output is quantifiable, the quality differences of the output cannot be measured. These imperfections may bias the results considerably. Since the choice of output and input measures are critically important for DEA results, the next section discusses the measures in detail.