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

Producer Price Index Manual
in response to changes in their relative prices. In the
absence of information about quantities or revenues
within an elementary aggregate, an ideal index can
be estimated only when certain special conditions
are assumed to prevail.
9.32 There are two special cases of some interest.
The first case is when producers continue to
produce the same relative quantities whatever the
relative prices. Producers prefer not to make any
substitutions in response to changes in relative
prices. The cross elasticities of supply are zero. The
technology by which inputs are translated into outputs
in economic theory is described by a production
function, and a production function with such a
restrictive reaction to relative price changes is described
in the economics literature as Leontief.
With such a production function, a Laspeyres index
would provide an exact measure of the ideal economic
index. In this case, the Carli index calculated
for a random sample of products would provide an
estimate of the ideal economic index that the products
are selected with probabilities proportional to
the population revenue shares. 1
9.33 The second case occurs when producers
are assumed to vary the quantities they produce in
inverse proportion to the changes in relative prices.
The cross-elasticities of supply between the different
products they produce are all unity, the revenue
shares remaining the same in both periods. Such an
underlying production function is described as
Cobb-Douglas. With this production function, the
Geometric Laspeyres 2 index would provide an exact
measure of the ideal index. In this case, the Jevons
index calculated for a random sample of products
would provide an unbiased estimate of the
ideal economic index provided that the products are
selected with probabilities proportional to the population
expenditure shares.
1 It might appear that if the products were selected with
probabilities proportional to the population quantity shares,
the sample Dutot would provide an estimate of the population
Laspeyres. However, if the basket for the Laspeyres index
contains different kinds of products whose quantities are
not additive, the quantity shares, and hence the probabilities,
are undefined.
2 The Geometric Laspeyres is a weighted geometric average
of the price relatives, using the revenue shares in the
earlier period as weights. (The revenue shares in the second
period would be the same in the particular case under consideration).
9.34 From the economic approach, the choice
between the sample Jevons index and the sample
Carli index rests on which is likely to approximate
more closely the underlying ideal economic index—in
other words, whether the (unknown) crosselasticities
are likely to be closer to unity or zero,
on average. In practice, the cross-elasticities could
take on any value ranging up to +∞ for an elementary
aggregate consisting of a set of strictly homogeneous
products—that is, perfect substitutes 3 . It
may be conjectured that for demand-led industries
where producers produce less of a commodity
whose relative price has increased to meet the reduced
quantity demanded, the average cross elasticity
is likely to be closer to unity. Thus the Jevons
index is likely to provide a closer approximation to
the ideal economic index than the Carli index. In
this case, the Carli index must be viewed as having
an upward bias. However, there are some establishments
in industries, including utilities, in which
supply is relatively unresponsive to demand
changes, and the Carli index would be more appropriate,
given that sampling is with probability proportional
to base-period revenue shares. And, yet
again, there would be establishments in industries
in which quantities produced increase as prices increase
and, with probability sampling proportional
to base-period revenues, neither the Carli nor the
Jevons index would be appropriate from the economic
approach.
9.35 The insight provided by the economic approach
is that the Jevons and Carli indices can be
justified from the economic approach depending on
whether a significant amount substitution is more
likely than no substitution, especially as elementary
aggregates should be deliberately constructed to
group together similar products that are close substitutes
for each other.
9.36 The Jevons index does not imply, or assume,
that revenue shares remain constant. Obviously,
the Jevons can be calculated whatever
changes do or do not occur in the revenue shares in
practice. What the economic approach shows is that
if the revenue shares remain constant (or roughly
constant), then the Jevons index can be expected to
provide a good estimate of the underlying ideal
3 It should be noted that in the limit when the products
really are homogeneous, there is no index number problem,
and the price “index” is given by the ratio of the unit values
in the two periods, as explained below.
220