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Abstract
This article explores with extensive computational and statistical analyses the impact that correlation and data translation have, independently, on the average data envelopment analysis (DEA) efficiency score of a data set. The article explores three types of correlations, (a) between inputs and outputs, (b) among inputs only, and (c) among outputs only. The results suggest that the degree of correlation between the inputs and outputs tends to affect average efficiency scores. High correlations between inputs and outputs tend to be associated with high efficiency scores on the average. If correlation between inputs and outputs is relatively high, the degree of correlation between inputs or between outputs is not relevant; at the most, higher correlation among inputs or among outputs tends to be associated with slightly lower average efficiency scores. When correlation between inputs and outputs is close to zero, the average efficiency score of a data set is usually small, independently of how much correlation there is among inputs only or among outputs only. With respect to data translation, an important contribution of this article is to provide the function that characterizes the effect that regular data translations have on the average efficiency score of a data set. This effect is a function of the coefficients of variation of the DEA attributes (the inputs and outputs). Specifically, the average of the inverse of the coefficients of variation can be used to model the impact of regular data translation on average efficiency scores.
Acknowledgments
We thank the reviewers for their constructive comments, which helped improving this paper. The idea of using the coefficient of variation to somehow measure translation away from the origin was suggested by Anthony L. Patti, a colleague of one of the authors of this paper. We thank him for the idea.