DEA Cobb–Douglas frontier and cross‐efficiency

The current paper examines the cross‐efficiency concept in data envelopment analysis (DEA). While cross‐efficiency has appeal as a peer evaluation approach, it is often the subject of criticism, due mainly to the use of DEA weights that are often non‐unique. As a result, cross‐efficiency scores are routinely viewed as arbitrary in that they depend on a particular set of optimal DEA weights generated by the computer code in use at the time. While imposing secondary goals can reduce the variability of cross‐efficiency scores, such approaches do not completely solve the problem of non‐uniqueness, and meaningful secondary goals can lead to computationally intractable non‐linear programs. The current paper proposes to use the units‐invariant multiplicative DEA model to calculate the cross‐efficiency scores. This allows one to calculate the maximum cross‐efficiency score for each DMU in a converted linear model, and eliminates the need for imposing secondary goals.