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

Producer Price Index Manual
⎡
⎢
⎢⎣
(( 4/2)
× 3+
4)
(3 + 2)
⎤
⎥ = 2.00
⎥⎦
and long-run comparisons for June:
⎡
⎢
⎢⎣
(( 5/2)
× 3+
5)
(3 + 2)
⎤
⎥ = 2.50 .
⎥⎦
7.209 A note of caution is required here. The
comparisons use an imputed value for product B in
April and also an imputed one for May. The price
comparison for the second term in equation (7.35),
for the current versus immediately preceding period,
use imputed values for product B. Similarly,
for the January to June results, the May to June
comparison uses imputed values for product B for
both May and June. The pragmatic needs of quality
adjustment may demand this. If comparable replacements,
overlap links, and resources for explicit
quality adjustment are unavailable, an imputation
must be considered. However, using imputed
values as lagged values in short-run comparisons
introduces a level of error into the index
that will be compounded with their continued use.
Long-run imputations are likely to be preferable to
short-run changes based on lagged imputed values
unless there is something in the nature of the industry
that cautions against such long-run imputations.
There are circumstances when the respondent
may believe the missing product is missing
temporarily, and the imputation is conducted under
the expectation that production will subsequently
continue, a wait-and-see policy is adopted under
some rule—three months, for example—after
which it is deemed to be permanently missing.
These are the pragmatic situations that require imputations
to extend over consecutive periods.
These circumstance promote lagged imputed values
to compare against current imputed values.
This is cautioned against, especially over a period
of several months. There is an intuition that the period
in question should not be extensive. First, the
effective sample size is being eaten up as the use
of imputation increases. Second, the implicit assumptions
of similar price movements inherent in
imputations are less likely to hold over the longer
run. Finally, there is some empirical evidence, albeit
from a different context, against using imputed
values as lagged actual values. (See Feenstra and
Diewert’s 2001 study using data from the U.S. Bureau
of Labor Statistics for their International Price
Program.)
7.210 The short-run approach described above
will be developed in the next section, where
weighted indices are considered. The practice of
estimating quality-adjusted prices is usually at the
elementary product level. At this lower level, the
prices of products may subsequently be missing
and replacements with or without adjustments and
imputations are used to allow the series to continue.
New products and varieties are also being
introduced; the switching of sales between sections
of the index becomes prevalent. The turmoil of
changing quality is not just about the maintaining
of similar price comparisons but also about the accurate
reweighting of the mix of what is produced.
Under a Laspeyres framework, the bundle is held
constant in the base period, so any change in the
relative importance of products produced is held to
be of no concern until the next rebasing of the index.
Yet capturing some of the very real changes
in the mix of what is produced requires procedures
for updating the weights. This was considered in
Chapter 5. The concern here is with a higher-level
procedure equivalent to the short-run adjustments
discussed above. It is one particularly suited to
countries where resource constraints prohibit the
regular updating of weights through regular household
surveys.
H.3 Single-stage and two-stage indices
7.211 Consider aggregation at the elementary
level (Chapter 6). This is the level at which prices
are collected from a representative selection of establishments
across regions in a period and compared
with the matched prices of the same products
in a subsequent period to form an index for a good.
Lamb is an example of a good in an index. Each
price comparison is equally weighted unless the
sample design gave proportionately more chance
of selection to products with more sales. The elementary
price index for lamb is then weighted, and
combined with the weighted elementary indices for
other products to form the PPI. A Jevons elementary
aggregate index, for example, for period t + 6
compared with period t is given as
N
t+
6 T
(7.36) PJ ( pi / pi
)
≡ ∏ .
i∈ N( t+ 6) ∩N( t)
194