# 24 Theory Using Dea Models to Measure

• Ing Kristína Vincová
• Published 2005

#### Abstract

BIATEC, Volume XIII, 8/2005 Ratios rank among the most simple methods. Their drawback is that they evaluate just a handful of indicators and cannot influence overall corporate efficiency. As an example, we may cite income per unit of costs. Nonparametric methods include Data Envelopment Analyses (DEA) and the Free Disposal Hull (FDH). We use them to measure technical (technological) efficiency. Technical efficiency looks at the level of inputs or outputs. Being technically efficient means to minimise inputs at a given level of outputs, or maximise outputs at a given level of inputs. Parametric methods of efficiency measurement include the Stochastic Frontier Approach (SFA), Thick Frontier Approach (TFA) and Distribution Free Approach (DFA). These methods measure economic efficiency. Economic efficiency is a broader term than technical efficiency. It covers an optimal choice of the level and structure of inputs and outputs based on reactions to market prices. Being economically efficient means to choose a certain volume and structure of inputs and outputs in order to minimise cost or maximise profit. Economic efficiency requires both technical efficiency and efficient allocation. While technical efficiency only requires input and output data, economic efficiency requires price data as well. DEA is a nonparametric method. It is a linear programming model, assuming no random mistakes, used to measure technical efficiency. Efficient firms are those that produce a certain amount of or more outputs while spending a given amount of inputs, or use the same amount of or less inputs to produce a given amount of outputs, as compared with other firms in the test group. FDH is another nonparametric and nonstochastic method, which can be seen as a generalised DEA model with variable returns to scale. This particular model does not require the estimated efficiency boundary to have a convex shape. The SFA econometric model presents a method assuming two error elements. In this approach, inefficiency is assumed to have asymmetrical distribution, usually a half normal distribution and random error is expected to have standard symmetrical distribution. SFA deals with the problem that not all deviations from criteria are due to a lack of efficiency.They may also occur as a result of misfortune (fortune) or measurement errors. TFA compares the average efficiency of a group of firms, rather than trying to estimate efficiency thresholds. DFA relies on average variations of a cost function estimated on a data set to construct a cost efficiency threshold. This method requires no specific form of distribution or average efficiency of each firm. The objective of this paper is to suggest possible ways for productive units to measure their efficiency. To that end, a variety of analysis, synthesis and comparison methods were used. The paper focuses on efficiency measurement by means DEA models, which can be broken up into certain subcategories. The DEA methodology gives us a tool to estimate “relative” efficiency of a chosen entity in a given group of units and criteria. The theory is demonstrated on a simple numerical and graphical example.

### Cite this paper

@inproceedings{Vincov200524TU, title={24 Theory Using Dea Models to Measure}, author={Ing Krist{\'i}na Vincov{\'a}}, year={2005} }