Estimating the impact of contextual variables on the productivity: An enhanced slack-based DEA model.

The contextual variable is an important issue that makes an indispensable impact on the productivities of decision making units (DMUs). Analyzing the contribution of such factors to productivity differences is an intriguing area of research in data envelopment analysis (DEA). We first investigate whether and how contextual variables impact performances of the DMUs based on slack-based measurement. We extend the implicit assumption of prior studies and suggest that contextual variables can be a catalyst to increase the productivity. Impact and error factors, which are derived from regression analysis and stochastic frontier analysis (SFA), are defined to better represent the composition of two contradictory impacts, catalyst and depressant, of contextual variables. A statistical analysis is provided to identify the significance of such impacts and recognize multi-collinearity among contextual variables. The two factors are also moderated flexibly by decision makers in accordance with various production scenarios. Accordingly, original inputs and outputs are appropriately adjusted. Further, modified slack-based DEA models are proposed to incorporate DEA and regression analysis within an integrated framework. Several properties and propositions are presented to better describe the characteristics of the models. An empirical example is shown to verify the feasibility of the proposed approach.