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A global Malmquist productivity index
Jesús T. Pastora, C.A. Knox Lovell
Economics Letters. Volume 88, Issue 2, August 2005, Pages 266–271
The geometric mean Malmquist productivity index is not circular, and its adjacent period components can provide different measures of productivity change. We propose a global Malmquist productivity index that is circular, and that gives a single measure of productivity change.

A global Malmquist-Luenberger productivity index

A global cost Malmquist productivity index