Fractional regression models for second stage DEA efficiency analyses
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Data envelopment analysis (DEA) is commonly used to measure the relative efficiency of decision-making units. Often, in a second stage, a regression model is estimated to relate DEA efficiency scores to exogenous factors. In this paper, we argue that the traditional linear or tobit approaches to second-stage DEA analysis do not constitute a reasonable data-generating process for DEA scores. Under the assumption that DEA scores can be treated as descriptive measures of the relative performance of units in the sample, we show that using fractional regression models is the most natural way of modeling bounded, proportional response variables such as DEA scores. We also propose generalizations of these models and, given that DEA scores take frequently the value of unity, examine the use of two-part models in this framework. Several tests suitable for assessing the specification of each alternative model are also discussed.
KeywordsSecond-stage DEA Fractional data Specification tests One outcomes Two-part models
JEL ClassificationC12 C13 C25 C51
The authors thank the editor, an associate editor and the referees for valuable comments that helped to substantially improve the paper. Financial support from Fundação para a Ciência e a Tecnologia is also gratefully acknowledged (grant PTDC/ECO/64693/2006).
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