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Article

Estimation of cost efficiency in non-parametric frontier models

The paper proposes a bootstrap methodology for estimating cost efficiency in data envelopment analysis. We consider the conventional concept of Fare, Grosskopf and Lovellcost efficiency, for which our algorithm re-samples “naive” input-oriented efficiency scores, rescales original inputs to bring them to the frontier, and then re-estimates cost efficiency scores for the rescaled inputs. Next, we examine Tone cost efficiency, where input prices vary across producers. Here we show that the direct modification on bootstrap algorithms by Simar and Wilson are applicable. We consider cases both with the absence and presence of environmental variables (i.e. input variables not directly controlled by firms). The bootstrap methodology exploits these assumptions: 1) the sample are i.i.d. random variables with the continuous joint probability density function with support over production set; 2) the frontier is smooth; and 3) the probability of observing firms on the frontier approaches unity with an increase in sample. The results of simulations for a multi-input, multi-output Cobb–Douglas production function with correlated outputs, and correlated technical and cost efficiency, show consistency of our proposed algorithm, even for small samples. Finally, we offer real data estimates for the Japanese banking industry in 2013. Our package “rDEA,” developed in the R language, is available from the GitHub and CRAN repository.