The problem with normalizing preferences that change in a cost-of-living index

There are new proposals for prices indexes that attempt to correct for what they consider bias in standard indexes from changes in consumer preferences But these proposals have a fundamental problem that changes in preferences between two periods cannot be identified by data on prices and quantities with only a normalization. This paper shows that the required normalization is not free so that an arbitrary choice of normalization can yield any desired index result. In fact, a normalization using the Sato-Vartia weights yields a Sato-Vartia index, implying exactly zero bias.