Alternative weighting schemes for the aggregate Malmquist productivity index: A theoretical and empirical comparison

In this paper, we present a number of alternative weighing schemes, which are obtained by combining different aggregator functions, i.e. arithmetic, harmonic and geometric, with different metrics, i.e. values of distance functions or efficiency scores, that result in the same value of the aggregate (input- and output-oriented) Malmquist productivity index. Our results indicate that first, in the output-oriented model the value of the aggregate Malmquist productivity index depends on the way efficiency is measured and thus, the aggregation weights will be different depending on whether the Farrell or the Färe, Grosskopf and Lovell (FGL) technical efficiency index is used (this is not an issue in the input-oriented model). Using panel farm-level data, we provide empirical evidence on this difference when inappropriate weighting schemes are used. Second, weighting schemes based on actual rather potential (input or output) shares are computationally less demanding.