Abstract
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.
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Notes
See Duan (1983) for a seminal paper on the consequences for prediction of using logged dependent variables.
Note that, under the assumption that S(·) is an invertible function, we may write \(L\left( x\theta \right) =S\left\{ S^{-1}\left[ L\left( x\theta \right) \right] \right\} \), where \( S^{-1}\left[ L\left( x\theta \right) \right] \) is a nonlinear function of xθ that can be approximated by a polynomial.
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Acknowledgments
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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Ramalho, E.A., Ramalho, J.J.S. & Henriques, P.D. Fractional regression models for second stage DEA efficiency analyses. J Prod Anal 34, 239–255 (2010). https://doi.org/10.1007/s11123-010-0184-0
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DOI: https://doi.org/10.1007/s11123-010-0184-0