Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation

Abstract

This paper provides a formal statistical basis for the efficiency evaluation techniques of data envelopment analysis (DEA). DEA estimators of the best practice monotone increasing and concave production function are shown to be also maximum likelihood estimators if the deviation of actual output from the efficient output is regarded as a stochastic variable with a monotone decreasing probability density function. While the best practice frontier estimator is biased below the theoretical frontier for a finite sample size, the bias approaches zero for large samples. The DEA estimators exhibit the desirable asymptotic property of consistency, and the asymptotic distribution of the DEA estimators of inefficiency deviations is identical to the true distribution of these deviations. This result is then employed to suggest possible statistical tests of hypotheses based on asymptotic distributions.