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

9. PPI Calculation in Practice
Table 9.2. Properties of Main Elementary Aggregate Index Formulas
Formula
Formula properties
Carli – Arithmetic mean
of price relatives
Dutot – Relative of
arithmetic mean prices
Jevons – Geometric
mean of price relatives
Proportionality yes yes yes
Change-of-units of
measurement yes no yes
Time reversal no yes yes
Transitivity no yes yes
Allows for substitution no no yes
weight given to pepper in the Dutot index by more
than 28 times. The price of pepper relative to salt is
inherently arbitrary, depending entirely on the
choice of units in which to measure the two goods.
In general, when there are different kinds of products
within the elementary aggregate, the Dutot index
is unacceptable conceptually.
9.29 The Dutot index is acceptable only when
the set of products covered is homogeneous, or at
least nearly homogeneous. For example, the Dutot
index may be acceptable for a set of apple prices,
even though the apples may be of different varieties,
but not for the prices of different kinds of
fruits, such as apples, pineapples, and bananas,
some of which may be much more expensive per
item or per kilo than others. Even when the products
are fairly homogeneous and measured in the
same units, the Dutot index’s implicit weights may
still not be satisfactory. More weight is given to the
price changes for the more expensive products, but
they may well account for only small shares of the
total revenue within the aggregate, in practice. Purchasers
are unlikely to buy products at high prices if
the same products are available at lower prices.
9.30 It may be concluded that from an axiomatic
viewpoint, both the Carli and the Dutot indices, although
they have been and still are widely used by
statistical offices, have serious disadvantages. The
Carli index fails the time reversal and transitivity
tests. In principle, it should not matter whether we
choose to measure price changes forward or backward
in time. We would expect the same answer,
but this is not the case for the Carli index. Chained
Carli indices may be subject to a significant upward
bias. The Dutot index is meaningful for a set of
homogeneous products but becomes increasingly
arbitrary as the set of products becomes more diverse.
On the other hand, the Jevons index satisfies
all the tests listed above and also emerges as the
preferred index when the set of test is enlarged, as
shown in Chapter 20. From an axiomatic point of
view, the Jevons index is clearly the index with the
best properties, even though it may not have been
used much until recently. The Jevons index also allows
for some substitution effects consistent with a
unitary elasticity of substitution. There seems to be
an increasing tendency for statistical offices to
switch from using Carli or Dutot indices to Jevons.
B.2.2 Economic approach to elementary
price indices
9.31 The objective of the economic approach is
to estimate for the elementary aggregates an “ideal”
(or “true”) economic index—that is, one consistent
with the economic theory of revenue-maximizing
producers explained in Section F of Chapter 20.
The products for which respondents provide prices
are treated as a basket of goods and services produced
by establishments to provide revenue, and
producers are assumed to arrive at their decision
about the quantities of outputs to produce on the basis
of revenue-maximizing behavior. As explained
in Chapters 1, 15, and 17, an ideal theoretical economic
index measures the ratio of revenues between
two periods that an establishment can attain
when faced with fixed technologies and inputs.
Changes in the index arise only from changes in
prices. The technology is assumed to be held fixed,
although the revenue-maximizing producer can
make substitutions between the products produced
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