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

Producer Price Index Manual
tion, consumer ignorance, or rationing, or some
kind of temporary disequilibrium. Informed producers
with unrestricted production possibilities
would not sell at a lower price if they had the opportunity
to sell exactly the same product at a
higher price. It is tempting to assume, therefore,
that the products are not really homogeneous and
that the observed price differences must be due to
quality differences of some kind or another, but imperfections
in producer and consumer markets are
widespread and cannot be assumed away a priori.
1.157 As explained in Section B of Chapter 20,
when a single product is sold at different prices, the
price of that product for PPI purposes is the unit
value, defined as total sales divided by total quantities:
that is, the quantity-weighted average price.
The price relative for the product is the ratio of the
unit values in the two periods. This may be affected
by a change in the pattern of products that sell at
high and low prices as well as by changes in the individual
prices.
1.158 If the representative sampled products are
selected with probabilities proportional to the quantities
sold at the different prices in the first period, a
simple (unweighted) arithmetic average of their
prices will provide an estimate of the unit value in
the first period. The Dutot index is the ratio of the
simple arithmetic average prices in the two periods.
However, given that the two sets of prices are perfectly
matched—that is, geared to the pattern of
production in the first period only—the Dutot cannot
take account of any changes in the patterns of
production between the two periods and may not
provide an unbiased estimate of the ratio of the unit
values. As shown in Section F of Chapter 20, the
sample Dutot with probabilities proportional to
quantities sold in the first period may be expected
to approximate to a Laspeyres-type index in which
the quantity weights are fixed, by definition. It does
not provide a satisfactory estimate of a unit-value
index in which the relative quantities do change.
Moreover, this approximated Laspeyres-type index
is not a conventional Laspeyres index because the
quantities do not refer to different products, or even
different qualities, but to different quantities of exactly
the same product sold at different prices.
1.159 In practice, even though producers’ choices
may be restricted because of their production technology,
buyer-seller relationships, market ignorance,
and other market imperfections, they may
switch production toward products sold at high
prices and away from those at low prices, as market
conditions change and restrictions on choice are
eased. The Dutot index, based on matched prices,
cannot take account of such switches and may tend
to understate the rise in the unit values for this reason.
Alternatively, it may be that the demand side
dictates market behavior, with establishments responding
to demand by increasing production of
low-priced products. When the ratio of the unit values
changes because purchasers, or at least some of
them, succeed in switching from establishments
selling at high prices to establishments selling at
low prices, the failure of PPIs to take account of
such switches leads to the Dutot index overstating
the fall in the unit-value index.
I.5.2 Heterogeneous elementary aggregates
1.160 In practice, most elementary aggregates are
likely to contain a large number of products that are
similar but not identical. Assuming producers are
informed and have a perfectly flexible set of production
possibilities, the relative prices may then be
expected to reflect producer’s marginal rates of
substitution. Within the same elementary aggregate,
the different products will often be close substitutes
for each other, often being no more than marginally
different qualities of the same generic product, so
that the quantities produced may be expected to be
quite sensitive to changes in relative prices.
1.161 Using an economic approach, it is possible
to ask what is the best estimate of the “true” economic
index, for the elementary aggregate. Bearing
in mind, however, that no information on quantities
and revenues is available within the aggregate, it is
necessary to resort to considering certain hypothetical
special cases. Suppose that producers react to
purchasers’ preferences; as demand increases for a
relatively low-priced product, producers produce
more of it. Assume purchasers have so-called
Cobb-Douglas preferences, which imply that the
cross-elasticities of substitution between the different
products are all unity. The quantity relatives
vary inversely with the price relatives, so that their
revenue shares and the establishment’s revenues
remain constant. The true economic index can then
be shown to be a weighted geometric average of the
price relatives, the weights being the revenue
shares—which, as just noted, are the same in both
periods. Now, suppose that the products whose
prices are sampled are randomly selected with
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