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

7. Treatment of Quality Change
7.204 At this unweighted level of aggregation, it
can be seen that there is no difference between the
long-run and short-run results when products are
not missing, comparable replacements are available,
explicit adjustments are made for quality, or
the overlap method is used. The separation of
short-run (most recent month-on-month) and longrun
changes may have advantages for quality assurance
to help spot unusual short run price
changes. But this is not the concern of this chapter.
The short-run approach does, however, have advantages
when imputations are made.
H.2 Implicit short-run comparisons
using imputations
7.205 The use of the short-run framework has
been considered mainly for temporarily missing
values, as outlined by Armknecht and Maitland-
Smith (1999) and Feenstra and Diewert (2001).
However, similar issues arise in the context of
quality adjustment. Consider again Table 7.5, but
this time there is no replacement product C and
product A’s prices have been changed to trend upward.
product B is again missing in April. A longrun
imputation for product B in April is given
by 3.5 × 3= 5.25. The price change is thus
2
(5.25 + 3.5) / 5 = 1.75 , or 75 percent. One gets the
same result as from simply using product A (3.5/2
= 1.75), since the implicit assumption is that price
movements of product B, had it continued to exist,
would have followed those of A. However, the assumption
of similar long-run price movements
may in some instances be difficult to support over
long periods. An alternative approach would be to
use a short-run framework whereby the imputed
price for April is based on the (overall) mean price
change between the preceding and current period,
that is, 3.5 × 4= 5.6 in the example. above In this
2.5
case, the price change between March and April is
(5.6 + 3.5)/(2.5 + 4) = 1.40. This is combined with
the price change between January and March:
(6.5/5) = 1.30 making the price change between
January and April 1.30 × 1.40 = 1.82 , an 82 percent
increase.
7.206 Consider why the short-run result of 82
percent is larger than the long-run result of 75 percent.
The price change for A between March and
April of 40 percent, on which the short-run imputation
is based, is larger than the average annual
change of A, which is just over 20 percent. The extent
of any bias from this approach was found in
the previous section to depend on the ratio of missing
values and the difference between the average
price changes of the matched sample and the quality-adjusted
price change of the product that was
missing, had it continued to exist. The short-run
comparison is to be favored if the assumption of
similar price changes is considered more likely to
hold than the long-run one.
7.207 There are data on price changes of the
product that is no longer available—product B in
Table 7.5—up to the period preceding the period
in which it is missing. In Table 7.5, product B has
price data for January, February, and March. The
long-run imputation makes no use of such data by
simply assuming that price changes January to
April are the same for B as for A. Let the data for
B’s prices in Table 7.5, (second to last row) now
be 3, 4, and 6 in January, February and March, respectively,
instead of 3, 3, and 4. The long-run estimate
for B in April is 5.25 as before. The estimated
price change between March and April for B
is now a fall from 6 to 5.25. A short-run imputation
based on the price movements of A between
March and April would more correctly show an increase
from 6 to (3.5/2.5) × 6 = 8.4.
7.208 There may, however, be a problem with
the continued use of short-run imputations. Returning
to the data for A and B in Table 7.5, consider
what happens in May. Adopting the same short-run
procedure, the imputed price change is given in
Table 7.5 as 4/3.5 × 5.6 = 6.4 and for June as (5/4)
× 6.4 = 8. In the former case, the price change
from January to May is
( )
( )
( )
( )
⎡ 6.4 + 4 ⎤ ⎡ 5.6 + 3.5 ⎤
× = 2.08
⎢⎣ 5.6 + 3.5 ⎥⎦ ⎢⎣ 3 + 2 ⎥⎦
and in the case of June
( )
( )
( )
( )
⎡ 8+ 5 ⎤ ⎡ 6.4+
4 ⎤
× = 2.60
⎢⎣ 6.4 + 4 ⎥⎦ ⎢⎣ 3 + 2 ⎥⎦
against long-run comparisons for May:
193