Alternative Indexes for Multiple Comparisons of Quantities and Prices

It is well known that binary indexes are not generally suitable for making multiple comparisons of quantities and/or prices because they fail a transitivity test. A common solution to the problem involves a geometric averaging procedure attributed to Elteto and Koves (1964) and Szulc (1964). However, so-called EKS indexes fail an identity test. This paper constructs indexes for multiple comparisons within an aggregate quantity-price framework. Such indexes satisfy nine fundamentally important tests: weak monotonicity, identity, commensurability, proportionality, time-space reversal, transitivity, circularity, and two homogeneity tests. A numerical example is used to illustrate that indexes widely used by national statistical agencies are biased. For example, chained Tornqvist and EKS indexes indicate that two identical quantity vectors differ by more than 2%. Three alternative indexes (Lowe, geometric Young and Fare-Primont) plausibly take the value one.