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

Producer Price Index Manual
also are bounds for a more generally applicable
true index.
It follows that some symmetric average of these
bounds is justified from economic theory.
1.91 The approach from economic theory is thus
first to develop theoretical index number formulas
based on what are considered to be reasonable
models of economic behavior by the producer. This
approach is very different from the others considered
here. A mathematical representation of the
production activity—whereby capital and labor
conjoin to turn intermediate inputs into outputs—is
required. Also, an assumption of optimizing behavior
(cost minimization or revenue maximization),
along with other assumptions, is required so that a
theoretical index can be derived that is “true” under
these conditions. The economic approach then examines
practical index number formulas such as
Laspeyres, Fisher, and Törnqvist, and considers
how they compare with “true” formulas defined under
different assumptions. Three theoretical formulations
will be examined—each, in principle, requiring
different assumptions about the optimizing
behavior of the firm. None can be practically calculated
(for reasons that will be explained). The first
approach to an economic theoretical producer price
index is the concept of the fixed-input output price
index. This index is a ratio of hypothetical revenues
over the two periods being compared, say periods 0
and 1, that the revenue-maximizing establishment
could realize, where the technology and inputs to
work with were fixed to be the same for both of the
periods. An establishment that, for example, doubles
its revenue using a fixed technology and inputs,
effectively doubles its prices. The theoretical
index is a ratio of revenues, so it incorporates substitution
effects as more revenue is obtained as
firms substitute toward higher-priced products. The
theoretical index wishes to have as its period 1
quantities the results of the firm changing the mix
of output it produces in response to relative price
changes. But there is a dilemma: only price changes
should be reflected, and by allowing quantities to
change in this way pure price changes would not be
measured. So the theoretical index fixes the amount
that can be produced by holding the technology and
inputs at some constant level. The firm can change
its output mix but must use constant inputs and
technology. Note that there is an entire family of
theoretical price indices depending on which period’s
reference technology and inputs are held constant:
fixed period 0 technology and primary inputs,
fixed period 1 technology and primary inputs, or
some average of the two.
1.92 Theoretical fixed-output input price indices
may also be defined. These are the ratio of hypothetical
intermediate input costs that the costminimizing
establishment must pay in order to produce
a set of outputs, again with technology and
primary inputs fixed to be the same for the comparison
in both periods.
1.93 The measurement of gross domestic product
(GDP) using the production approach involves
calculating the value added by the industry. Value
added is the difference between the value of output
produced by industries and the value of the intermediate
inputs used. The value added by each industry
is then summed along with taxes less subsidies
on products to provide an estimate of GDP. An
important use of the PPI is to deflate the values of
output and inputs at current period prices to estimate
value added at constant prices. In Chapter 17
the economic approach is first used to define a theoretical
output price index, intermediate input price
index, and value-added deflator for a single establishment.
Aggregation is then undertaken over establishments
in order to define national counterparts
to these establishment price indices in Chapter 18.
E.1 Theoretical output price indices
1.94 The theoretical output price index between
periods 0 and 1 is the ratio of the maximum revenues
that the establishment could attain when faced
with period 0 and 1 prices using a fixed, given
technology and a fixed set of inputs. Consider a
theoretical index in which period 0 technology and
inputs are held constant, the theoretical counterpart
to the Laspeyres index. What is required for the
numerator of the ratio is to generate what the period
1 quantities would be, holding the production process
and inputs constant in period 0 after the change
in relative prices from the period 0 technology and
inputs. This in turn requires a mechanism to generate
these hypothetical period 1 quantities from the
fixed period 0 technology and inputs. In the economic
approach the technology of a firm or industry
is described in terms of a production (possibility)
function, which tells us the maximum amount
of output(s) that can be produced from a given set
of inputs. If the values of all the inputs to a firm or
industry were given, the production function would
be able to generate all possible combinations of
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