Randomizing DEA Efficiency Scores with Beta Distribution

Since the original publication on Data Envelopment Analysis (DEA) by Charnes et al. (1978), a considerable amount of research publications have appeared in decision science literature, a significant portion of which focusing on efficiency and productivity in the banking sector. A comprehensive survey of bank efficiency studies could be found in Fethi and Pasiouras (2010). They have examined bank branch efficiencies in more than 30 studies over the period 1998-2009. A shortcoming of DEA modeling that has come under criticism is that input/output data in DEA are treated as deterministic, but in reality, these data are contaminated with statistical noise, and therefore, efficiency score of each decision making unit (DMU) does not reflect reality. In this chapter, we propose a method to randomize efficiency scores by treating each score as an order statistic of an underlying Beta distribution. Then, we apply this method to a small set of banks from Sri Lanka and show how to do the randomization. To our knowledge, to date, very few authors have discussed similar randomization in an efficiency study.