Statistical hypothesis testing for returns to scale using data envelopment analysis

Data envelopment Analysis (DEA) is a kind of non-parametric and non-statistical tools for measuring technological efficiencies. Recently, several researchers adopt this method to evaluate the efficiencies of firms, public utilities, and so on. Because this method is not based on the statistical setup, we cannot test hypothesis where the production function should be assumed. In this paper, we propose several tests for returns to scale using different DEA models. We construct test statistics for the hypothesis about the returns to scale in production technology without any assumption on the true distribution of the technical inefficiencies. We conduct a simulation study on the size and power of the proposed test statistics under several conditions: Cobb-Douglas production function with half-normally and exponentially distributed error terms.