Circular Error in Price Index Numbers Based on Scanner Data

Abstract

Differences between chain and base methods (or strategies) are analyzed. This is a preliminary paper that concentrates on numerical results and new ideas. Omitted proofs will appear in later papers. As in title, we use the term circular or chain error. We do not use milder terms as drift or deviation in the identity or circular test, because it is definitely an error of the chain index. Chain error is a norm of all proper index numbers formulas (except Lowe, Jevons and their derivatives which are not proper) and it vanishes only in special circumstances. Our main claim is that chain error is almost zero only if all its links are described by the same almost ideal demand theory. This is demonstrated for a comprehensible set of both contingently biased and excellent index numbers.

Keywords: Base and chain strategy, chain error (CE), contingently biased and excellent index number formulas, ideal demand theory, price-links, time reversal test (TRT), circular test (that is transitivity) (CT), multi period identity test (MPIT), path independence test (PIT), homothetic price-link.