Decomposing Allocative Efficiency for Multi-Product Production Systems

Data envelopment analysis (DEA), the non-parametric approach to measuring efficiency, was widely used in the literature as a linear programming model. Since the DEA is non-parametric linear program model, the estimated efficiency might be biased if there is data aggregation in DEA. It is proposed that both the inter-input aggregation and inter-output aggregation will make the estimated technical efficiency biased downwardly. Following some discussions on the technical efficiency bias caused by data aggregation in data envelopment analysis, this study presents the up-ward bias in the allocative efficiency caused by inter-output aggregation. However, hitherto, we have not observed any studies on considering how to utilize this character of DEA in methodology extensions for multi-output production system. Therefore, this paper originally proposes that the ‘traditional’ allocative efficiency can be decomposed for multi-product system. Then, the method to obtain decomposed allocative efficiency components is provided. In fact, the meaning of results from this paper is outside the DEA method, and the generality of the findings in this paper can provide useful information for researchers who concern the decision-making process in allocating resources for multi-product production system. Finally, an empirical example to show how to use the method in decomposing allocative efficiency for multi-product production system is also presented in the paper. In addition, some empirical situations (in both the agricultural sector and the industrial sector) are provided to tell us when we should use this method. Although this paper only provides a two-stage allocating process, the method developed here can be easily extended for the three-stage allocating process or even more complicated production system.