Superlative approximation of the Luenberger-Hicks-Moorsteen productivity indicator: Theory and application - Frederic Ang; Pieter Jan Kerstens (University of Copenhagen, Department of Food and Resource Economics (IFRO), 2018)
Consisting of the difference between an output indicator and an input indicator, the Luenberger-Hicks-Moorsteen (LHM) productivity indicator allows straightforward interpretation. However, it requires estimation of distance functions that are inherently unknown. This paper shows that a simple Bennet profit indicator is a superlative approximation of 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 the 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.
Keywords: C43; D21; D22; D24; 330; Productivity and competitiveness; Bennet; Luenberger-Hicks-Moorsteen; superlative approximation; Italian food and beverages sector