How to measure the impact of environmental factors in a nonparametric production model

The measurement of technical efficiency of decision making units is useful for making comparisons and informing managers and policy makers on existing differentials and potential improvements across a sample of analyzed units. The step further is to relate the obtained efficiency estimates to some external or environmental variables which may influence the production process and hence, affect the performance evaluation and explain the efficiency differentials. Conditional efficiency measures (Daraio and Simar, 2005; 2007a), including conditional FDH, conditional DEA, conditional order−m and conditional order− , have been recently introduced and became rapidly a useful tool to investigate the impact of external-environmental factors on the performance of Decision Making Units in a nonparametric framework. In this paper, we clarify what can be learned by analyzing these conditional efficiency scores, showing that the impact of these factors on the production process can have different facets: impact on the attainable set in the input × output space, and/or impact on the distribution of the inefficiency scores. The approach proposes statistical inference on the level of the impact, using up-to-dated bootstrap algorithms for which we prove the consistency. The procedure is illustrated through simulated samples and with a real data set in the Banking industry.