Chain indices and path independence

Methods are considered to calculate a set of consistent price index numbers from an inconsistent set of chained index numbers. The inconsistencies are due to the existence of cycles in the price index graph cycles.  The initial index numbers are calculated using an index formula, to the user’s choice. It is only required to satisfy a few simple consistency conditions. This does not include transitivity. One method (due to Hill) uses spanning trees to solve (or rather: sidestep) the inconsistency problem. The second method seeks to adjust the initial values in such a way that the new index numbers satisfy a transitivity criterion, and are close to the original index numbers. The approach in the present paper is inspired by levelling in land surveying.

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