Chain Fisher volume index - Methodology

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Transformation of volume indexes

Laspeyres volume index

The best known volume index is Laspeyres. For this index, weighting is done using prices from a pre-determined base year.

(1)
where:	LQt/o is the Laspeyres quantity index po is the price at time o qt is the quantity at time t qo is the quantity at time o

...or, in a version that can be chained:

(2)

where the periods o are replaced by t-1. By using the identity C = pq (value equals price multiplied by quantity), formula (2) can be expressed in a more usable form:

(2a)

so:

(2b)

hence:

(3)

Paasche volume index 

As well as referring to a previous period, a volume index can be based on prices from the current period. This is known as a Paasche index.

(4)
where:	PQt/o is the Paasche quantity index pt is the price at time t qt is the quantity at time t qo is the quantity at time o

...or, in a version that can be chained:

(5)

By performing the same substitutions that we did with the Laspeyres index, we get:

(5a)

and:

(5b)

hence:

(6)

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