## 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 AE_{0 }= 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 EE_{0 }= (OA/OC) = (OA/OB) × (OB/OC) = TE_{0 }× AE_{0}. Again, all of these three measures are bounded by zero and one. 0

mance improvement?

•

Which production facilities are the most effi- cient in my organization?

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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?

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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:

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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.

the

scores

between

two

•

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.

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