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

1. An Introduction to PPI Methodology
prices are collected over a succession of time periods.
An elementary price index is therefore typically
calculated from two sets of matched price observations.
It is assumed in this Section that there
are no missing observations and no changes in the
quality of the products sampled, so that the two sets
of prices are perfectly matched. The treatment of
new and disappearing products, and of quality
change, is a separate and complex issue that is discussed
in detail in Chapters 7, 8, and 21 of the
Manual.
I.1 Heterogeneity of products within
an elementary aggregate
1.137 If a number of different representative
products are selected for pricing, the set of products
within an elementary aggregate cannot be homogeneous.
Even a single representative product may not
be completely homogeneous, depending upon how
tightly it is specified. This topic is considered in
more detail in Chapters 5–7. The degree of heterogeneity
of the sampled products must be explicitly
taken into account in the calculation of an elementary
index.
1.138 When the quantities are not homogeneous,
they cannot be meaningfully added from an economic
viewpoint, and their prices should not be averaged.
Consider again the example of salt and
pepper, which might be representative products
within an elementary aggregate. Pepper is an expensive
spice sold in very small quantities such as
ounces or grams, whereas salt is relatively cheap
and sold in much larger quantities, such as pounds
or kilos. A simple arithmetic average of, say, the
price of a gram of pepper and the price of a kilo of
salt is an arbitrary statistic whose value depends
largely on the choice of the quantity units. Choosing
the same physical unit of quantity, such as a
kilo, for both does not resolve the problem, because
both the average price and the change in the average
price would be completely dominated by the
more expensive product, pepper, even though producers
may obtain more revenue from salt. In general,
arithmetic averages of prices should be taken
only when the corresponding quantities are homogeneous
and can be meaningfully added.
I.2 Weighting
1.139 As already noted, it is assumed in this section
that there are no quantities or revenues available
to weight the prices, or the price relatives, used
to calculate an elementary index. If they were available,
it would usually be preferable to use them to
decompose the elementary aggregate into smaller
and more homogeneous aggregates.
1.140 However, some system of weighting may
have been implicitly introduced into the selection of
the sampled products by the sample design used.
For example, the establishments from which the
prices are collected may have been selected using
probabilities of selection that are proportional to
their sales or some other variable.
I.3 Interrelationships between different
elementary index formulas
1.141 Valuable insights into the properties of
various formulas that might be used for elementary
price indices may be gained by examining the numerical
relationships between them, as explained in
Section D of Chapter 20. There are two basic options
for an elementary index:
• To average the price relatives—that is, the ratios
of the matched prices;
• To calculate the ratio of average prices in each
period.
1.142 It is worth recalling that for any set of positive
numbers the arithmetic average is greater than
or equal to the geometric average, which in turn is
greater than or equal to the harmonic average, the
equalities holding only when the numbers are all
equal. Using these three types of average, the ranking
of the results obtained by the second method are
predictable. It should also be noted that the ratio of
geometric averages is identical with the geometric
average of the ratios. The two methods give the
same results when geometric averages are used.
1.143 As explained in Section C of Chapter 20,
there are several elementary price indices that might
possibly be used. Using the first of the above options,
three possible elementary price indices are:
• The arithmetic average of the price relatives,
known as the Carli index, or P C ; the Carli is the
unweighted version of the Young index.
• The geometric average of the price relatives,
known as the Jevons index, or P J ; the Jevons is
the unweighted version of the geometric Young
index.
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