A Choice of an Index under Inefficiency: Tornqvist or Fisher Index? Evidence from Simulation

Abstract

This study addresses a choice of quantity index when inefficiency exists. Performing simulations, we show that 1) the finding from the previous literature that the Fisher index and the Tornqvist index approximate each other is only a special case when inefficiency is negligible, 2) the Tornqvist index begins to deviate as inefficiency increases because the Tornqvist index uses the average cost shares as a weight in the calculation, and 3) the Tornqvist index eventually suffers from the Simpson's paradox, in which the average of two higher numbers are lower than the average of two lower numbers, when the factor substitutability is large. From these results, we conclude that the Fisher index is preferred to the Tornqvist index when any inefficient use of factors is suspected.