On piecewise loglinear frontiers and log efficiency measures

Chang and Guh (1995) provide a so-called units invariant distance efficiency measure and argue that Sueyoshi and Changʹs (1989) remedy for Charnes et al. (1982, 1983) is not units invariant. However, we show that (i) Chang and Guh (1995) misunderstand Sueyoshi and Changʹs (1989) remedy, and (ii) the loglinear frontier determined by the Chang and Guhʹs distance efficiency measure, which is for the case of constant output and a linearly homogeneous production technology, is the same as obtained from Charnes et al. (1982, 1983). Chang and Guh (1995) ignore the fact that it is the constant output case, rather than the distance efficiency measure, that produces units invariance. We show that (i) their constant output assumption implies units invariance of the resulting loglinear efficient frontier, and (ii) their distance efficiency measure is developed and works under an implied condition of units invariance. We examine invariance in loglinear DEA models and correct erroneous calculations and claims in Chang and Guhʹs (1995) paper.