Model misspecification in Data Envelopment Analysis

Abstract

The use of Data Envelopment Analysis for estimating comparative efficiency has become widespread, and there has been considerable academic attention paid to the development of variants of the basic DEA model. However, one of the principal weaknesses of DEA is that - unlike statistically based methods - it yields no diagnostics to help the user determine whether or not the chosen model is appropriate. In particular, the choice of inputs and out-puts depends solely on the judgement of the user. The purpose of this paper is to examine the implications for efficiency scores of using a misspecified model. A simple production process is set up. Simulation models are then used to explore the effects of applying misspecified DEA models to this process. The phenomena investigated are: the omission of significant variables; the inclusion of irrelevant variables; and the adoption of an inappropriate variable returns to scale assumption. The robustness of the results is investigated in relation to sample size; variations in the number of inputs; correlation between inputs; and variations in the importance of inputs. The paper concludes that the dangers of misspecification are most serious when simple models are used and sample sizes are small. In such circumstances, it is concluded that it will usually be to the modeller's advantage to err on the side of including possibly irrelevant variables rather than run the risk of excluding a potentially important variable from the model.