Technical Efficiency Measurement by Data Envelopment Analysis
The Farrell output-orientated efficiency measures would be defined as follows. In Figure 4, the dis- tance AB represents technical inefficiency. That is, the amount by which outputs could be increased without requiring extra inputs. Hence a measure of o u t p u t - o r i e n t a t e d t e c h n i c a l e ffi c i e n c y i s t h e r a t i o T E = OA/OB. If we have price information then we can draw the isorevenue line DD’, and define the alloca- tive efficiency to be AE0 = OB/OC which has a rev- enue increasing interpretation (similar to the cost re- ducing interpretation of allocative inefficiency in the input-orientated case). Furthermore, one can define overall economic efficiency as the product of these two measures EE0 = (OA/OC) = (OA/OB) × (OB/OC) = TE0 × AE0. Again, all of these three measures are bounded by zero and one. 0
Which production facilities are the most effi- cient in my organization?
If all my operations were to perform according to best practice, how many more service outputs could I produce and by how much could I reduce my resource inputs, and in what areas?
What is the optimum scale for my operations and how much would I save if all my facilities were the optimum size?
Advantages and Limitations of DEA
Operationalizing the Concepts
There are several ways to use the data from the sam- ple to try and approximate the smooth curve in Figure 1. Early attempts used ordinary least squares regres- sion techniques that plot an average curve through the sample points. However, this was not satisfactory be- cause an individual organization’s efficiency was com- pared with an average level of performance in the sam- ple rather than an estimate of best practice within the sample. This led to attempts to approximate best prac- tice in the sample by estimating frontiers. The two techniques used to estimate the frontier are DEA and stochastic frontier analysis. The focus in this intro- duction is on DEA, which is a deterministic means of constructing a “piece-wise linear” approximation to the smooth curve of Figure 1 based on the available sample. In simple terms, the distribution of sample points is observed and a “kinked” line is constructed around the outside of them, “enveloping” them (hence the term data envelopment analysis).
What Questions can DEA help us answer?
Fried, Lovell and Schmidt (1994) listed the following as questions that DEA can help to answer for man- agers:
How do I select appropriate role models to serve
as possible benchmarks for a program of perfor-
The main advantage of DEA is that it can readily incorporate multiple inputs and outputs to calculate technical efficiency. By identifying the “peers” for or- ganizations that are not observed to be efficient, it pro- vides a set of potential role models that an organization can look to, in the first instance, for ways of improving its operations. However, like any empirical technique, DEA is based on a number of simplifying assumptions that need to be acknowledged when interpreting the re- sults of DEA studies. DEA’s main limitations include the following:
Being a deterministic rather than statistical tech-
nique, DEA produces results that are partic-
ularly sensitive to measurement error. only measures efficiency relative to best tice within the particular sample. Thus, it
DEA prac- is not
meaningful to compare different studies.
DEA scores are sensitive to input and output specification and the size of the sample. De- spite these limitations, data envelopment anal- ysis is a useful tool for examining the efficiency of government service providers. Just as these limitations must be recognized, so must the po- tential benefits of using DEA (in conjunction with other measures) be explored to increase our understanding of public sector performance and potential ways of improving it.
Alliance Journal of Business Research