Abstract
We consider the use of the non-Archimedean infinitesimal epsilon in DEA-CCR models. The application of interest is defined by the performance measure of the Brazilian Agricultural Research Corporation research centers. We characterize an assurance region for the non-Archimedean element and suggest a value for it. Types of DMUs are compared using fractional regression models and quasi maximum likelihood inference. We conclude that the research centers aimed at studying specific agricultural products are dominant. The classic DEA-CCR performance measures and the solution provided by non-Archimedeanmodel have Spearman correlation over 90%.
Highlights
1 INTRODUCTION Since 1996, the Brazilian Agricultural Research Corporation (Embrapa) monitors the production of its research centers with the use of an evaluation system based on a single performance output and three inputs
The results were obtained via SAS programming, adapting the macro ORDEA of Emrouznejad & Ho (2012)
The model is based on a three dimensional output vector, constructed from the observed ranks of several production variables grouped into three performance categories: technicalscientific publications, technical publications, and other production activities
Summary
Since 1996, the Brazilian Agricultural Research Corporation (Embrapa) monitors the production of its research centers with the use of an evaluation system based on a single performance output and three inputs. The existence of outputs or inputs with null weights in the multiplier solution of the DEA-CCR model suggests the use of a non-Archimedean constant in the evaluation process. As a referee pointed out, the use of non-Archimedean constants may lead to inadequacies in the sense that the Pareto efficient target in the solution does not correspond to the target used to measure efficiency. Ramalho et al (2010) suggest the use of the Papke & Wooldridge (1996) approach for two stage regressions This approach is of our concern here, since the contextual variables are DMU types, unrelated to the performance score and non endogenous. Gomes et al (2008) give indication that the correlation induced by the design is not statistically significant for analysis of variance inferences when DEA responses are subjected only to treatment effects, validating, in this context, the fractional regressions of Ramalho et al (2010).
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