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

7. Treatment of Quality Change
tion requirements for a strategy for such quality
adjustment in the face of a statistical metadata system.
D. Implicit Methods
D.1 Overlap Method
7.80 Consider an example where the items are
sampled in January and prices compared over the
remaining months of the year. Matched comparisons
are undertaken between the January prices
and their counterparts in successive months. Five
products are assumed to be sold in January with
1 1 1 1
prices p1, p2,
p
5,
p
6
,and p 1 8
(Table 7.2, part a).
Two types of similar products are produced in the
industrial group concerned, A and B. An index of
the elementary level is required for the overall
price change of these two product types. At this
level of aggregation, the weights can be ignored
assuming only one quote is taken on each product.
A price index for February compared with January
= 100.0 is straightforward in that prices of products
1, 2, 5, 6 and 8 are used and compared only by
way of the geometric mean of price ratios, the Jevons
index (which is equivalent to the ratio of the
geometric mean in February over the geometric
mean in January—see Chapter 20). In March, the
prices for products 2 and 6—one of type A and one
of type B—are missing,.
7.81 In Table 7.2 the lower part (b) is a numerical
counterpart of the upper part (a). further illustrating
the calculations. The overlap method requires
prices of the old and replacement products
to be available in the same period. In Table 7.2(a),
product 2 has no price quote for March. Its new
replacement is, for example, product 4. The overlap
method simply measures the ratio of the prices
of the old and replacement product prices in an
overlap period. In this example, the period is February,
and the old and replacement products are
products 2 and 4, respectively. This is taken to be
an indicator of their quality differences. The two
approaches outlined in Section C.3.2 are apparent:
either to insert a quality-adjusted price in January
for product 4 and continue to use the replacement
product 4 series, or continue the product 2 series
by patching in quality-adjusted product 4 prices.
Both yield the same answer. Consider the former.
For a Jevons geometric mean from January to
March for establishment A only, assuming equal
weights of unity
1 3 3 1 3 2 2 1
(7.1) P (( ) ) 12
J
( p , p ) = ⎡ p1 / p1 × p4 / p4 / p2 × p ⎤
2
⎣
= [ 6/4 x 8/ ((7.5 / 6) x 5)] 1/2
= 1.386.
7.82 Note that the comparisons are long-run
ones.,. that is, they are between January and the
month in question. The short-run modified
Laspeyres framework provides a basis for shortrun
changes based on data in each current month
and the immediately preceding one. In Table 7.2(a)
and (b), the comparison for product type A would
first be undertaken between January and February
using products 1 and 2. The result would be multiplied
by the comparison between February and
March using items 1 and 4. Still, this implicitly
uses the differences in prices in the overlap in February
between items 2 and 4 as a measure of this
quality difference. It yields the same result as before:
1 1
2 2
⎡5 6⎤ ⎡6 8 ⎤
⎢ × 1.386
4 5⎥ × ⎢ × =
5 7.5⎥
⎣ ⎦ ⎣ ⎦
The advantage of recording price changes for
January to October in terms of January to September
and September to October is that it allows the
compiler to compare immediate month-on-month
price changes for data editing purposes. Moreover,
it has quite specific advantages for the use of imputations
as discussed in Sections D.2 and D.3 for
which different results arise for the long and shortrun
methods. A fuller discussion of the long-run
and short-run frameworks is undertaken in Section
H.
⎦
157