A Luenberger-Hicks-Moorsteen productivity indicator: its relation to the Hicks-Moorsteen productivity index and the Luenberger productivity indicator

Introducing a new difference-based Luenberger-Hicks-Moorsteen productivity indicator, this contribution establishes theoretically its relations with some existing ratio- and difference-based productivity indexes and indicators. The first main result is an approximation proposition stating that the logarithm of the Hicks-Moorsteen productivity index is about equal to the Luenberger-Hicks-Moorsteen productivity indicator. Secondly, we also establish the specific conditions under which the Luenberger-Hicks-Moorsteen indicator equals the recently introduced Luenberger indicator and compare these to the conditions governing the relations between ratio-based Hicks-Moorsteen and Malmquist indices.