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

Producer Price Index Manual
Dec00: m01 00( Dec00)
Dec00: m01
(9.20) I = ∑ w ⋅I
i
i
,
00( Dec00)
where Wi
are the weights from 2000 price
updated to December 2000. At the time when
weights for 2001 are available, this is replaced by
the long-term link
Dec00: Dec01 01( Dec00)
Dec00: Dec01
(9.21) I = ∑ w ⋅I
i
i
,
01( Dec00)
where Wi
are the weights from 2001 price
backdated to December 2000. The same set of
weights from 2001 price updated to December 2001
are used in the new short-term link for 2002,
(9.22)
Dec01: m02 01( Dec01)
Dec01: m02
I = ∑ w ⋅I
i
i
.
9.133 Using this method, the movement of the
long-term index is determined by contemporaneous
weights that refer to the same period. The method is
conceptually attractive because the weights that are
most relevant for most users are those based on
production patterns at the time the price changes actually
take place. The method takes the process of
chaining to its logical conclusion, at least assuming
the indices are not chained more frequently than
once a year. Since the method uses weights that are
continually revised to ensure that they are representative
of current production patterns, the resulting
index also largely avoids the substitution bias that
occurs when the weights are based on the production
patterns of some period in the past. The method
may therefore appeal to statistical offices whose objective
is to estimate an economic index.
9.134 Finally, it may be noted that the method
involves some revision of the index first published.
In some countries, there is opposition to revising a
PPI once it has been first published, but it is standard
practice for other economic statistics, including
the national accounts, to be revised as more upto-date
information becomes available. This point is
considered below.
C.8 Decomposition of index
changes
9.135 Users of the index are often interested in
how much of the change in the overall index is attributable
to the change in the price of some particular
product or group of products, such as petroleum
or food. Alternatively, there may be interest in
what the index would be if food or energy were left
out. Questions of this kind can be answered by decomposing
the change in the overall index into its
constituent parts.
9.136 Assume that the index is calculated as in
equation (9.10) or equation (9.11). The relative
change of the index from t – m to t can then be written
as
(9.23)
∑
∑
w ⋅I ⋅I
1 −1.
I w I
0: t
b 0: t−m t−mt
:
I
i i i
− =
0: t−m b 0: t−m
i
⋅
i
Hence, a subindex from t – m to 0 enters the higherlevel
index with a weight of
(9.24)
w ⋅I w ⋅I
∑
b 0: t−m b 0: t−m
i i i i
=
b 0: t−m 0: t−m
wi
⋅ Ii
I
The effect on the higher-level index of a change in
a subindex can then be calculated as
w ⋅ I ⎛ I ⎞
(9.25) Effect = ⋅ − ⎟
⎠
.
b 0: t−m 0: t
i i i
1
0: t−m ⎜ 0: t−m
I ⎝Ii
b
wi
t:0 0: t−m
0: − ( I
t m i
Ii
).
i
= ⋅ −
I
With m = 1, it gives the effect of a monthly change;
with m = 12, it gives the effect of the change over
the past 12 months.
9.137 If the index is calculated as a chained index,
as in equation (9.15), then a subindex from t –
m enters the higher-level index with a weight of
(9.26)
0 0: t−m
0: k
i
⋅ ( i i )
−
( )
0 kt : −m
wi
⋅ I w I I
i
= .
kt : −m 0: t m 0: k
I I I
The effect on the higher-level index of a change in
a subindex can then be calculated as
0
w
kt : −m
I
0 0: t 0: t−m
w ⎛ − ⎞
i
Ii Ii
= ⋅⎜ 0: k ⎟.
⎝ Ii
⎠
i kt : kt : −m
(9.27) Effect = ⋅( Ii
−Ii
)
0: t−m 0: k
( I I )
.
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