A model suggestion for elasticity measurement in data envelopment analysis: An application in agriculture

Data Envelopment Analysis (DEA) is a widely used non-parametric technique for assessing relative efficiency of decision making units (DMUs). It provides efficiency scores of DMUs according to their performances and separates DMUs as efficients and inefficients. Context-Dependent DEA is a version of DEA which assings DMUs to the efficient frontiers with respect to current performance levels of them. In other words, Context-Dependent DEA clustering DMUs and create different efficient frontiers for each cluster. Context-Dependent DEA also provides attainable targets for DMUs in the short-term and long-term periods. Elasticity is a measure of response of the variables to the proportional change of the other variables in given technology. Elasticity can only used for DMUs which are situated on efficient frontiers. It also provides information about returns to scale (RTS) characteristics of DMUs. This research proposes a method to measure elasticities on efficient frontiers determined by Context- Dependent DEA. The research pursues three main objectives that can be summarized as follows. First of all; we make an efficiency assessment of units with DEA and Context-Dependent DEA and assign these units efficient frontier layers with respect to their performance levels. Secondly, we measure elasticities on determined levels and identify returns to scale (RTS) characteristics of units under various scenarios. Finally, the implementation of the proposed methodology to Turkish farming sector. The empirical application deals with agricultural farms that operate in the Aegean Region of Turkey and Farm Accountancy Data Network (FADN) data is used in the analyses of the farms. The results reveal that the proposed method enables us to obtain findings about all of the production possibility set. In general, the application represents illustration of the proposed method and it involves elasticity measurements with comprehensive sensitivity analyses of production possibility set and the findings for the farms in the Aegean Region.