The Differential Approach to Superlative Index Number Theory

Abstract

Diewert’s “superlative” index numbers, defined to be exact for second-order aggregator functions, unify index number theory with aggregation theory but have been difficult to identify. We present a new approach to finding elements of this class. This new approach, related to that advocated by Henri Theil, transforms candidate index numbers into growth rate form and explores convergence rates to the Divisia index. Because the Divisia index in continuous time is exact for any aggregator function, any discrete time index number that converges to the Divisia index and that has a third-order remainder term is superlative.