Abstract
This paper first introduces the allocative and profit efficiency in the presence of the negative data and then presents a new circular index to measure the productivity change of decision making units (DMUs) for the case that the dataset contains the inputs and/or outputs with the negative values in data envelopment analysis (DEA). The proposed index is decomposed into four components in the two stages. The range directional model (RDM) and the proposed efficiencies are used to compute the proposed index and its components. The interpretations of the components are presented. Finally, a numerical example is organized to illustrate the proposed index and its components at three successive periods of time.
Highlights
The Malmquist productivity index which measures the productivity change over time was introduced by Caves et al [1]
Fare et al [2] developed the Malmquist productivity index that was based on data envelopment analysis (DEA)
By using Malmquist index, the productivity growth can be decomposed into the efficiency change and technical change components
Summary
The Malmquist productivity index which measures the productivity change over time was introduced by Caves et al [1]. The traditional DEA models can be applied to compute the Malmquist index with the nonnegative data. They cannot deal with the negative data. To investigate the productivity change of DMUs with the negative data, this paper defines the profit and allocative efficiency and introduces an index to measure the productivity changes of DMUs when some inputs and/or outputs are negative and the costs of inputs and the prices of outputs are available.
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