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

Producer Price Index Manual
on a fixed basket of goods and services. That the
Walsh index is both a superlative and a pure index
throws light on the interrelationships between the
theoretical output price index and pure price indices.
The distinctive feature of a Walsh index is not
just that the basket of goods and services is a simple
(geometric) average of the quantities in each of the
two periods; by being a geometric average, it also
assigns equal importance to the relative, as distinct
from the absolute, quantities. Such an index clearly
treats both periods symmetrically. 12 Pure price indices
do not have to diverge from the theoretical output
price index and are not inherently biased as estimators
of the theoretical index. Bias is only likely
to arise when the relative quantities used in a pure
price index favor one of the periods at the expense
of the other, as in a Laspeyres or Paasche index.
E.3.3 Representativity bias
1.110 That the Walsh index is a Lowe index that
is also superlative suggests that the bias in other
Lowe indices depends on the extent to which their
quantities deviate from those in the Walsh basket.
This can be viewed from another angle.
1.111 Because the quantities in the Walsh basket
are geometric averages of the quantities in the two
periods, equal importance is assigned to the relative,
as distinct from the absolute, quantities in both
periods. The Walsh basket may therefore be regarded
as being the basket that is most representative
of both periods. 13 If equal importance is attached
to the production patterns in the two periods,
the optimal basket for a Lowe index ought to be the
most representative basket. The Walsh index then
becomes the conceptually preferred target index for
a Lowe index.
1.112 Suppose that period b, whose quantities are
actually used in the Lowe index, lies midway between
0 and t. In this case, assuming fairly smooth
trends in the relative quantities, the actual basket in
period b is likely to approximate the most represen-
12 The Marshall-Edgeworth index (see Chapter 15) uses a
simple arithmetic average of the quantities, but the resulting
basket will be dominated by the quantities for one or other
of the periods if the quantities are larger, on average, in one
period than the other. The Marshall-Edgeworth is not a superlative
index.
13 The Walsh basket is the one that minimizes the sum of
the squares of the logarithmic deviations between the quantities
in the two actual baskets and those in the index basket.
tative basket. Conversely, the farther away that period
b is from the midpoint between 0 and t, the
more the relative quantities of b are likely to diverge
from those in the most representative basket.
In this case, the Lowe index between periods 0 and
t that uses period b quantities is likely to exceed the
Lowe index that uses the most representative quantities
by an amount that becomes progressively larger
the farther back in time period b is positioned.
The excess constitutes “bias” if the latter index is
target the index. The bias can be attributed to the
fact that the period b quantities tend to become increasingly
unrepresentative of a comparison between
0 and t the farther back period b is positioned.
The underlying economic factors responsible
are, of course, exactly the same as those that
give rise to bias when the target index is the economic
index. Thus, certain kinds of indices can be
regarded as biased without invoking the concept of
an economic index. Conversely, the same kinds of
indices that tend to emerge as being preferred,
whether or not the objective is to estimate an economic
index.
1.113 If interest is focused on short-term price
movements, the target index is an index between
consecutive time periods t and t + 1. In this case,
the most representative basket has to move forward
one period as the index moves forward. Choosing
the most representative basket implies chaining.
Similarly, chaining is also implied for the target
economic index t and t + 1. In practice, the universe
of products is continually changing as well. As the
most representative basket moves forward, it is possible
to update the set of products covered as well
as take account of changes in the relative quantities
of products that were covered previously.
E.3.4 Data requirements and calculation
issues
1.114 Because superlative indices require price
and revenue data for both periods and revenue data
are usually not available for the current period, it is
not feasible to calculate a superlative PPI, at least at
the time that a PPI is first published. In practice, it
may be necessary for the official index to be a
Laspeyres type index. However, in the course of
time more revenue data may become available,
enabling a superlative PPI to be calculated subsequently.
Some statistical offices may find it useful
to do so, without necessarily revising the original
official index. Comparing movements in the official
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