Sub-vector Efficiency analysis in Chance Constrained Stochastic DEA: An application to irrigation water use in the Krishna river basin, India

All deviations from the frontier is inefficiency in deterministic DEA (DDEA); thus making the DDEA unable to accommodate the measurement and specification errors. But, most of the production relationships are stochastic in nature with some inputs fixed in the short run. This paper addressed the above two issues by formulating a sub-vector efficiency model in a Stochastic DEA (SDEA) framework to analyze the efficiency of sub vector of inputs. The results illustrate that there is a wide scope for stochastic efficiency analysis. The overall efficiency in SDEA is higher than DDEA under both Constant and Variable Return to Scale frameworks. SDEA revealed that some efficient producers are not sub-vector efficient in our case study. Thus, overall efficiency oriented policy may not be sufficient for optimizing water use. The proposed model has limitations in terms of the degree of stochastic variability and the level of tolerance that the model can accommodate