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

1. An Introduction to PPI Methodology
probabilities proportional to their revenue shares in
the first period. As shown in Section F of Chapter
20, with this method of selection, the simple geometric
average of the sample price relatives—that
is, the Jevons index—may be expected to provide
an approximation to the underlying economic index.
1.162 However, for PPIs the assumption of unit
cross-product elasticities of substitution with equal
revenues in both periods is not consistent with producer
economic theory. Revenue-maximizing producers
will produce more of the sampled products
with above-average price increases, so their share
of revenue cannot be expected to be constant. Indeed
the Jevons index, in assuming constant revenue
shares, will understate price changes under
such revenue-maximizing behavioral assumptions.
The Jevons index allows implicit quantities to fall
as relative prices increase, to maintain equal revenue
share, rather than allowing an increase. There is
not an accepted unweighted price index number formula
that incorporates such substitution behavior,
although the Jevons index has been shown to be unsuitable
under producer revenue-maximizing assumptions.
1.163 Alternatively, suppose that the production
technology is such that, at least in the short term,
there is no substitution in response to relative price
changes, and the relative quantities remain fixed. In
this case, the true economic index would be a
Laspeyres-type index. If the products were sampled
with probabilities proportional to the revenue shares
in the first period, a simple arithmetic average of
the price relatives—that is, the Carli index—would
approximate to it 14 . However, assuming no substitution
is unreasonable and counterfactual in general,
although it may occur exceptionally.
1.164 Thus, using the economic approach, under
one set of conditions the Jevons index would provide
an approximation to the underlying economic
index, while under another set of conditions the
Carli index would do so. In most cases, the actual
conditions seem likely to be closer to those required
14 Notice that the Dutot index cannot be used when the
products are not homogeneous, since an arithmetic average
of the prices of different kinds of products is both arbitrary
and economically meaningless. If a Laspeyres index is estimated
as a simple average of the price relatives—that is, assuming
equal revenue shares—the implied quantities cannot
be equal because they vary inversely with the prices.
for the Jevons to estimate the underlying index than
for the Carli, since the cross-elasticities of substitution
seem much more likely to be close to unity
than zero for industries whose pricing behavior is
demand driven. Thus, the economic approach provides
some support for the use of Jevons rather than
Carli, at least in most situations. However, if producer
revenue-maximizing behavior is believed to
dominate an industry use of the Jevons index is not
supported.
1.165 Another alternative is suggested in Section
G of Chapter 20. If products are sampled according
to fixed revenue shares in each period, then the resulting
sample can be used with the Carli formula
(P C ) to estimate the Laspeyres index, and the harmonic
mean formula (P H ) to calculate the Paasche
index. By taking the geometric average of these two
formulas, as suggested by Carruthers, Sellwood,
Ward (1980), and Dalén (1992a), a Fisher index
would result:
(1.18) P CSWD
= P C
× P H
.
1.166 However, since statistical offices would
not have the revenue shares for the current period,
an approximation to the Fisher index is obtained by
assuming they are not too different from those used
in the base period 0. A similar assumption would
justify the use of a Jevons index (P J ,) as an approximation
to a Törnqvist index. Again recall, that
these approximations result when the observations
are sampled in proportion to revenue shares.
1.167 One lesson to be drawn is that, when trying
to decide on the most appropriate form of the price
index for an elementary aggregate, it is essential to
pay attention to the characteristics of the products
within the aggregate and not rely on a priori generalizations.
In particular, the Dutot index should be
used only when the products are homogeneous and
measured in exactly the same units. When the products
are heterogeneous, the choice between the
Carli and the Jevons index turns on the extent to
which, and the nature of, substitution behavior that
is likely to occur in response to relative price
changes. In many cases, the Jevons is likely to be
preferred. Because Jevons is also the preferred index
on axiomatic grounds, it seems likely to be the
most suitable form of elementary index in most
situations, although the circumstances underlying
its use should be carefully established.
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