The geometric mean version of the Malmquist productivity index does not satisfy the circular test, and its component adjacent period indexes can give different productivity change measures for the same data. A fixed-base version of the index solves both problems, but it is not independent of the base period. It has been argued that time-neutrality of technical change is necessary and sufficient for all three properties to hold. We show that time-neutrality is sufficient, but not necessary, for all three properties. We develop a weaker version of time-neutrality that is necessary and sufficient for all three properties to hold.
Malmquist productivity index Circularity Time-neutrality