A superlative indicator for the Luenberger-Hicks-Moorsteen productivity indicator: Theory and application

Consisting of the difference between an output indicator and an input indicator, the Luenberger-Hicks-Moorsteen (LHM) productivity indicator allows straightforward interpretation. However, its computation requires estimating distance functions that are inherently unknown. This paper shows that a computationally simple Bennet indicator is a superlative indicator for the LHM indicator when one can assume profit-maximizing behavior and the input and output directional distance functions can be represented up to the second order by a quadratic functional form. We also show that the Luenberger- and LHM-approximating Bennet indicators coincide for an appropriate choice of directional vectors. Focusing on a large sample of Italian food and beverages companies for the years 1995−2007, we empirically investigate the extent to which this theoretical equivalence translates into similar estimates. We find that the Bennet indicator is a close empirical alternative to the LHM indicator for the sample.