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

1. An Introduction to PPI Methodology
proach in itself does not determine the form of the
index number. There are several stochastic indices
to choose from, just as there are many possible universes.
However, as already noted, the elementary
prices from which most aggregate price indices are
constructed usually have to be based on samples of
prices, and the stochastic approach may provide
useful guidance on how best to estimate them.
E. The Economic Approach
1.87 The economic approach differs from the
previous approaches in an important respect: quantities
are no longer assumed to be independent of
prices. If, for example, it is assumed that firms behave
as revenue maximizers, it follows that they
would produce more of products with aboveaverage
price changes in, say, period 1 compared
with period 0. As a result, the revenue shares in period
1 from such products will increase, and therefore,
their weights. This behavioral assumption
about the firm, as it switches production to higherpriced
products, allows something to be said about
what “true” indices should be and the suitability of
different index number formulas. For example, the
Laspeyres index uses fixed period 0 revenue shares
to weight its price relatives and ignores the substitution
of production toward products with higher relative
price changes in period 1. It will thus understate
aggregate price changes—be biased downward
against its true index. The Paasche index uses fixed
period 1 weights and ignores the initial revenue
shares in period 0. It will thus overstate aggregate
price changes—be biased upward against its true
index.
1.88 The economic approach can be seen to be
very powerful, since it has identified a type of bias
in Laspeyres and Paasche indices not apparent from
other approaches: substitution bias. Laspeyres and
Paasche indices ignore the change in weights as
producers substitute their production toward products
with above-average price increases. Yet the nature
of the bias arises from an assumption about the
behavior of producers—that they are revenue
maximizers. Consider an alternative assumption:
that producers respond to demand changes
prompted by purchasers buying less of products
with relatively high price changes. Products whose
price increases are, for example, above average will
see a falloff in demand leading to a falloff in production.
In this case the revenue shares or weights
of products with above-average price increases will
fall in period 1, and the fixed period 0 weighted
Laspeyres will overstate aggregate price changes—
it will be upward biased. This compares with the
Paasche index, which will understate aggregate
price changes—it will be downward biased. It is
shown in Chapter 17 that Laspeyres and Paasche
indices can under certain conditions act as bounds
on a more generally applicable “true” economic
theoretic index. The axiomatic approach in Section
C led to an index number formula that used an average
of the Laspeyres and Paasche indices, and
even at this early stage in the discussion, the economic
approach seems to provide further support.
1.89 The economic approach also identifies the
circumstances under which the conventionally used
Laspeyres index is appropriate. This would require
that the firm does not change its production configuration
in response to relative price changes, at
least over the short term of the price index comparisons.
Economic theory thus argues that the
Laspeyres index may be appropriate for industries
in which quantities are known not to respond to
relative price changes over the period of the price
comparisons. But it is more likely that this will be
the exception rather than the norm, and the theory
points to a requirement for a more generally applicable
index number formula.
1.90 The PPI indices considered here include
output, input, and value-added price indices (deflators),
and different assumptions arise in their formulation
from economic theory. In the output case,
an assumption is made that firms act to maximize
revenues, from a given input base. Firms substitute
toward products with relatively high price increases.
For the input price index, the concern is to
minimize the costs of purchased intermediate
goods. Firms substitute away from input products
with relatively high price increases. For the valueadded
deflator, the unusual use of negative weights
for the inputs is considered. The economic approach,
as shown in Chapter 17, demonstrates that:
• A substitution bias can exist when using
Laspeyres and Paasche formulas.
• The nature of the bias depends on the behavioral
assumptions of the firm, which will vary
between industries and the type of PPI index
required—input or output PPI.
• Laspeyres and Paasche indices act as bounds on
their true indices and, under certain conditions,
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