Fractional regression models for second stage DEA efficiency analyses

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 are 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.

The Impact of Regulatory and Supervisory Structures on Bank Risk and Efficiency: Evidence from Dual Banking System

“…The DEA model of data analysis with regard to bank efficiency has generally been favoured by most academics (Berger et al, 1993;Berger & Humphrey, 1997;Casu & Molyneux, 2000). Despite criticism from some academics (Simar & Wilson, 2011;Ramalho, Ramalho & Henriques, 2010) it is generally accepted by most academics that the DEA model is a sound technique for efficiency estimation. McDonald (2009) examined the second stage DEA efficiency analyses and found that there are good arguments for treating DEA efficiency scores as descriptive measures in a second stage analyses.…”

Vegetable diversification in cocoa-based farming systems Ghana

“…First, select one index from the four using factor analysis [20]. The second involves modelling each of the indices, testing each of them through inspection of model properties and rigorous tests such as P test, in order to first select the most appropriate functional form for each index, and then choose the best model from among the four selected models as the most appropriate model [10,36]. The effort involved in the latter which provides the same results as the former makes the former appear more efficient than the latter; hence, the former approach was selected for this study.…”

“…We follow Ramalho et al [36] by testing four functional forms in order to select one (best-bet) for discussion.…”

“…The generalised goodness-offunctional form (GGOFF) test [36,37] and P test [10] were accordingly employed. The estimation was accomplished using the STATA module developed by Ramalho [37].…”

“…Consequently, the GGOFF is used in place of the RESET test in this study. For an exposition of details on GGOFF, see for example [36,37].…”