Generalized quadratic revenue functions

In this paper we focus on the specification of revenue functions in their dual price space. We consider two distance functions–the Shephard output distance function and the directional output distance function–and define both in price space. The former is multiplicative in nature and satisfies homogeneity, whereas the latter is additive and satisfies the translation property. Functional equation methods yield the translog specification in the case of the Shephard distance function and a quadratic specification in the case of the directional distance function. Monte Carlo evidence suggests that the quadratic specification outperforms the translog in large samples and in true models with plenty of curvature.