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

1. An Introduction to PPI Methodology
can be compared with the nominal period 1 value at
current prices to provide, for bilateral comparisons,
an estimate of quantity change at constant period 1
prices. These results were devised for the establishment,
and it is also shown in Chapter 18 that
they hold on aggregationfor Laspeyres and Paasche
indices and fairly closely for the three main superlative
indices: Fisher, Törnqvist, and Walsh.
G. Illustrative Numerical Data
1.123 Chapter 19 presents numerical examples
using an artificial data set. The purpose is not to illustrate
the methods of calculation as such, but
rather to demonstrate how different index number
formulas can yield very different numerical results.
Hypothetical but economically plausible prices,
quantities, and revenues are given for six products
over five periods of time. In general, differences between
the different formulas tend to increase with
the variance of the price relatives. They also depend
on the extent to which the prices follow smooth
trends or fluctuate.
1.124 The numerical results are striking. For example,
the Laspeyres index over the five periods
registers an increase of 44 percent whereas the
Paasche falls by 20 percent. The two commonly
used superlative indices, Törnqvist and Fisher, register
increases of 25 percent and 19 percent, respectively,
an index number spread of only 6 points
compared with the 64 point gap between the
Laspeyres and Paasche. When the indices are
chained, the chain Laspeyres and Paasche register
increases of 33 percent and 12 percent, respectively,
reducing the gap between the two indices from 64
to 21 points. The chained Törnqvist and Fisher register
increases of 22.26 percent and 22.24, percent
respectively, being virtually identical numerically.
These results show that the choice of index formula
and method does matter.
H. Choice of Index Formula
1.125 By drawing on the index number theory
surveyed in Chapters 15–19 it is possible to decide
on the type of index number in any given set of circumstances.
However, there is little point in asking
what is the best index number formula for a PPI.
The question is too vague. A precise answer requires
a precise question. For example, suppose
that the principal concern of most users of PPIs is to
have the best measure of the current rate of factory
gate inflation. The precise question can then be
posed: what is the best index number to use to
measure the change between periods t – 1 and t in
the prices of the producer goods and services leaving
the factory between periods t – 1 and t
1.126 The question itself determines both the
coverage of the index and the system of weighting.
The establishments in question have to be those of
the country in question and not, say, those of some
foreign country. Similarly, the question refers to establishments
in periods t – 1 and t, not to establishments
five or ten years earlier. Sets of establishments
five or ten years apart are not all the
same, and their inputs and production technologies
change over time.
1.127 Because the question specifies goods and
services produced in periods t – 1 and t, the basket
of goods and services used should include all the
quantities produced by the establishments in periods
t – 1 and t, and only those quantities. One index
that meets these requirements is a pure price index
that uses a basket consisting of the total quantities
produced in both periods t – 1 and t. This is equivalent
to an index that uses a simple arithmetic mean
of the quantities in the two periods, an index known
as the Marshall-Edgeworth index. However, this
index has a slight disadvantage in that if domestic
production is growing, the index gives rather more
weight to the quantities produced in period t than
those in t – 1. It does not treat both periods symmetrically.
It fails Tests T7 and T8 listed in Chapter 16
on the axiomatic approach, the invariance to proportional
changes in quantities tests. However, if
the arithmetic mean quantities are replaced by the
geometric mean quantities, as in the Walsh index,
both tests are satisfied. This ensures that the index
attaches equal importance to the patterns of production,
as measured by relative quantities produced in
both t – 1 and t.
1.128 The Walsh index therefore emerges as the
pure price index that meets all the requirements. It
takes account of every single product produced in
the two periods. It utilizes all the quantities produced
in both periods, and only those quantities. It
gives equal weight to the patterns of production in
both periods. In practice, it may not be feasible to
calculate a Walsh index, but it can be used as the
standard by which to evaluate other indices.
1.129 The index theory developed in Chapters
15–17 demonstrates that the Fisher and the Törn-
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