Elasticity measurement on multiple levels of DEA frontiers: an application to agriculture

Recently, the elasticity of response measures revealing the marginal characteristics of efficient frontiers have been developed and generalized for different types of DEA production technologies. In theory, the elasticity measures can be calculated for the units on the efficient frontier that satisfy a selective radial efficiency assumption. This corresponds to a subset of the evaluated units. In this research, we propose to extend the elasticity measurement to the entire production possibility set (technology) by stratifying the units to different levels of efficient frontiers. The stratification idea is inspired by the commonly known context-dependent DEA based on the exclusion of efficient units at each iteration and obtaining multiple levels of frontiers. We build the proposed methodology on the idea that a DEA technology theoretically consists of several frontiers and calculating elasticity measures on all frontiers may provide additional information on the returns-to-scale (RTS) characteristics of all the units whether they are on the first-level frontier or not. The proposed methodology is presented in an empirical application using the Farm Accountancy Data Network (FADN) data of the agricultural farms operating in the Aegean Region of Turkey. The results reveal that the proposed method enables us to obtain a wider perspective on the RTS characterizations of DEA production technologies.