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

1. An Introduction to PPI Methodology
1.37 This has different implication for consumers
and producers. The theory of consumer behavior
indicates that consumers typically react to price
changes by substituting goods or services that have
become relatively cheaper for those that have become
relatively dearer. Thus they purchase smaller
quantities of the higher-priced products and more of
lower-priced ones. This is known as the substitution
effect, and it implies a negative correlation between
the price and quantity relatives. In this case the
Laspeyres CPI would be greater than the Paasche
CPI with the gap between them tending to widen
over time. 7 That the Laspeyres tends to rise faster
than the Paasche is a matter of concern to many
analysts and CPI users because it suggests that the
widely used Laspeyres index may have an upward
bias.
1.38 The theory of the firm indicates the opposite
behavior on the part of producers. As prices for
particular products begin to rise, producers will
shift production away from lower-priced, less profitable
products toward the higher-priced more profitable
ones. This type of substitution by producers
implies a positive correlation between price and
quantity relatives. In this case the Paasche PPI
would be greater than the Laspeyres PPI with the
gap between them widening over time. That the
Paasche tends to rise faster than the Laspeyres is a
matter of concern to many analysts and PPI users
because it suggests that the widely used Laspeyres
index may have a downward bias, a point taken up
later.
1.39 In practice, however, statistical offices often
do not calculate Laspeyres or Paasche indices
but instead calculate Lowe indices as defined in
equation (1.1). The question then arises of how the
Lowe index relates to the Laspeyres and Paasche
indices. It is shown in Section D.1 of Chapter 15
that if the there are persistent long-term trends in
relative prices and if the substitution effect for purchasers
is dominant, the Lowe index will tend to exceed
the Laspeyres, and therefore also the Fisher
and the Paasche. Assuming that the time period b is
7 If the revenue shares—that is, the weights associated with
the price relatives—happen to be the same in both periods,
the Laspeyres must be greater than the Paasche because a
weighted arithmetic average is always greater than a harmonic
average with the same weights. In order to maintain
the revenue shares intact, the substitution of the quantities in
response to changes in relative prices must be perfect.
prior to the time period 0, the ranking under these
conditions will be:
Lowe ≥ Laspeyres ≥ Fisher ≥ Paasche.
Moreover, the amount by which the Lowe exceeds
the other three indices will tend to increase, the further
back in time period b is in relation to period 0.
1.40 The positioning of period b is crucial.
Given the assumptions about long-term price trends
and substitution, a Lowe index will tend to increase
(decrease) as period b is moved backward (forward)
in time. While b may have to precede 0 when
the index is first published, there is no such restriction
on the positioning of b as price and quantity
data become available for later periods with the
passage of time. Period b can then be moved forwards.
If b is positioned midway between 0 and t,
the quantities are likely to be equirepresentative of
both periods, assuming that there is a fairly smooth
transition from the relative quantities of 0 to those
of t. In these circumstances, the Lowe index is
likely to be close to the Fisher and other superlative
indices and cannot be presumed to have either an
upward or a downward bias. These points are elaborated
further below and also in Section D.2 of
Chapter 15.
1.41 It is important that statistical offices take
these relationships into consideration in deciding
upon their policies. There are obviously practical
advantages and financial savings from continuing to
make repeated use over many years of the same
fixed set of quantities to calculate a PPI. However,
the amount by which such a PPI exceeds some conceptually
preferred target index, such as the economic
index discussed in Section E below, is likely
to get steadily larger the further back in time the period
b to which the quantities refer. Most users are
likely to interpret the difference as an upward bias. 8
A large bias may undermine the credibility and acceptability
of the index.
8 Of course, if producers are price takers from the market
and the demand shifts dominate, then producers will respond
by increasing the quantities produced of goods with higher
relative prices. The correlation between prices and quantities
in this instance will be positive, and the relationship among
the indices will be
Paasche ≥ Fisher ≥ Laspeyres ≥ Lowe,
and the bias interpreted as downward.
9