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

Producer Price Index Manual
1.57 The PPIs in some countries are, in fact, annual
chain Lowe indices of this general type, the
quantities referring to some year, or years, that precedes
the price reference period 0 by a fixed period.
For example,
• The 12 monthly indices from January 2000 to
January 2001, with January 2000 as the price
reference period could be Lowe indices based
on price updated revenues for 1998;
• The 12 indices from January 2001 to January
2002 are then based on price updated revenues
for 1999;
and so on with annual weight updates. The revenues
lag behind the January price reference period by a
fixed interval, moving forward a year each January
as the price reference period moves forward one
year. Although, for practical reasons, there has to be
a time lag between the quantities and the prices
when the index is first published, it is possible to
recalculate the monthly indices for the current later,
using current revenue data when they eventually
become available. In this way, it is possible for the
long-run index to be an annually chained monthly
index with contemporaneous annual weights. This
method is explained in more detail in Chapter 9. It
is used by one statistical office.
1.58 A chain index between two periods has to
be “path dependent.” It must depend on the prices
and quantities in all the intervening periods between
the first and last periods in the index series. Path
dependency can be advantageous or disadvantageous.
When there is a gradual economic transition
from the first to the last period with smooth trends
in relative prices and quantities, chaining will tend
to reduce the index number spreads among the
Lowe, Laspeyres, and Paasche indices, thereby
making the movements in the index less dependent
on the choice of index number formula.
1.59 However, if there are fluctuations in the
prices and quantities in the intervening periods,
chaining may not only increase the index number
spread but also distort the measure of the overall
change between the first and last periods. For example,
suppose all the prices in the last period return
to their initial levels in period 0, which implies
that they must have fluctuated in between, a chain
Laspeyres index does not return to 100. It will be
greater than 100. If the cycle is repeated, with all
the prices periodically returning to their original
levels, a chain Laspeyres index will tend to “drift”
further and further above 100 even though there
may be no long-term upward trend in the prices.
Chaining is therefore not advised when the prices
fluctuate. When monthly prices are subject to regular
and substantial seasonal fluctuations, for example,
monthly chaining cannot be recommended.
Seasonal fluctuations cause serious problems,
which are analyzed in Chapter 22. While a number
of countries update their revenue weights annually,
the 12 monthly indices within each year are not
chain indices but Lowe indices using fixed annual
quantities.
B.4.2 The Divisia index
1.60 If the prices and quantities are continuous
functions of time, it is possible to partition the
change in their total value over time into price and
quantity components following the method pioneered
by Divisia. As shown in Section E of Chapter
15, the Divisia index may be derived mathematically
by differentiating value (that is, price
times quantity) with respect to time to obtain two
components: a relative value-weighted price change
and relative value-weighted quantity change. These
two components are defined to be price and quantity
indices, respectively. The Divisia index is essentially
a theoretical index. In practice, prices can
be recorded only at discrete intervals even if they
vary continuously with time. A chain index may,
however, be regarded as a discrete approximation to
a Divisia index. The Divisia index itself offers no
practical guidance about the kind of index number
formula to choose for the individual links in a chain
index.
C. The Axiomatic Approach to
Index Numbers
1.61 The axiomatic approach to index numbers
is explained in Chapter 16. It seeks to decide the
most appropriate formula for an index by specifying
a number of axioms, or tests, that the index ought to
satisfy. It throws light on the properties possessed
by different kinds of indices, some of which are by
no means intuitively obvious. Indices that fail to
satisfy certain basic or fundamental axioms, or
tests, may be rejected completely because they are
liable to behave in unacceptable ways. The axiomatic
approach is also used to rank indices on the
basis of their desirable, and undesirable, properties.
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