On testing equality of distributions of technical efficiency scores

The challenge of the econometric problem in production efficiency analysis is that the very efficiency scores to be analyzed are unobserved. Recently, statistical properties have been discovered for a class of estimators popular in the literature, known as data envelopment analysis (DEA) approach. This opens a wide range of possibilities for a well-grounded statistical inference about the true efficiency scores from their DEA-estimates. In this paper we investigate possibility of using existing tests for equality of two distributions for such a context. Considering statistical complications pertinent to our context, we consider several approaches to adapt the Li (1996) test to the context and explore their performance in terms of the size and the power of the test in various Monte Carlo experiments. One of these approaches showed good performance both in the size and in the power, thus encouraging for its wide use in empirical studies.