Producer Price Index Manual: Theory and Practice ... - METAC

Producer Price Index Manual
Table 9.8. Calculation of a Chained Index
Index
Weight
1998
1998 Nov 02 Dec 02 Weight
2000
Dec 02 Jan 03 Feb 03 Mar 03
1998 = 100 Dec 2002 = 100
Elementary price indices
A 0.20 100.00 120.00 121.00 0.25 100.00 100.00 100.00 102.00
B 0.25 100.00 115.00 117.00 0.20 100.00 102.00 103.00 104.00
C 0.15 100.00 132.00 133.00 0.10 100.00 98.00 98.00 97.00
D 0.10 100.00 142.00 143.00 0.18 100.00 101.00 104.00 104.00
E 0.30 100.00 110.00 124.00 0.27 100.00 103.00 105.00 106.00
Total 100.00 119.75 124.90 100.00 101.19 102.47 103.34
Higher-level indices
G = A+B+C 0.60 100.00 120.92 122.33 0.55 100.00 100.36 100.73 101.82
H = D+E 0.40 100.00 118.00 128.75 0.45 100.00 102.20 104.60 105.20
Total 100.00 119.75 124.90 100.00 101.19 102.47 103.34
Chaining of higher-level indices to 1998 = 100
G = A+B+C 0.60 100.00 120.92 122.33 0.55 122.33 122.78 123.22 124.56
H = D+E 0.40 100.00 118.00 128.75 0.45 128.75 131.58 134.67 135.45
Total 100.00 119.75 124.90 124.90 126.39 127.99 129.07
• Chaining is intended to ensure that the individual
indices on all levels show the correct development
through time.
• Chaining leads to nonadditivity. When the new
series is chained onto the old as in equation
(9.15), the higher-level indices after the link
cannot be obtained as weighted arithmetic averages
of individual indices using the new
weights. 6 Such results need to be carefully explained
and presented.
9.115 An example of the calculation of a chain
index is presented in Table 9.8. From 1998 to December
2002, the index is calculated with the year
1998 as weight and price reference period. From
6 If, on the other hand, the index reference period is
changed and the index series before the link period are rescaled
to the new index reference period, these series cannot
be aggregated to higher-level indices by use of the new
weights.
December 2002 onward, a new set of weights is introduced.
The weights may refer to the year 2000,
for example, and may or may not have been price
updated to December 2002. A new fixed weight index
series is then calculated with December 2002 as
price reference month. Finally, the new index series
is linked onto the old index with 1998 = 100 by
multiplication to get a continuous index from 1998
to March 2003.
9.116 The chained higher-level indices in Table
9.8 are calculated as
(9.16)
00: t 98: Dec02 00( Dec02) Dec02:
t
I = I ⋅∑ wi
⋅Ii
.
Because of the lack of additivity, the overall
chained index for March 2003 (129.07), for example,
cannot be calculated as the weighted arithmetic
mean of the chained higher-level indices G and H
using the weights from December 2002.
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