I am trying to find an additive decomposition of a Tornqvist index - to measure the contribution of individual industries to sector-level productivity indexes - and I can find formulae for this, but not the explanation for what these are based on.
My initial intuition for the contribution of a particular industry to the overall sector's index is that we would calculate the index with and without the industry. If I do this I can derive a relatively simple decomposition.
From discussions with someone I work with, though, it appears that the more accepted way of thinking about contributions to an index is leaving the industry (or product, or whatever the subindex is) in the index, but with a 0 movement.
Can anyone point me to any literature on why/if this is the concept that should be applied?
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