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

21. Quality Change and Hedonics
Changing tastes and technologies
21.85 The estimates of the coefficients may
change over time. Some of this will be attributed to
sampling error, especially if multicollinearity is
present, as discussed below. But, in other cases, it
may be a genuine reflection of changes in tastes
and technologies. If a subset of the estimated coefficients
from a hedonic regression is to be used to
quality adjust a noncomparable replacement price,
then the use of estimated out-of-date coefficients
from some previous period to adjust the prices of
the new replacement model would be inappropriate.
There would be a need to update the indices as
regularly as the changes demanded. 32 For estimating
hedonic indices, the matter is more complicated.
The coefficients in a simple dummy timeperiod
model as in Section C.3 now have different
estimates of the parameters in each period. Silver
(1999), using a simple example, shows how the estimate
of quality adjusted price change from such a
dummy-variable model requires a reference basket
of characteristics. This is apparent for the hedonic
imputation indices where separate indices using
base-and current-period characteristics are estimated.
A symmetric average of such indices is
considered appropriate. A hedonic index based on
a time dummy variable implicitly constrains the
estimated coefficients from the base and current
periods to be the same. Diewert (2003) formalizes
the problem of choosing the reference characteristics
when comparing prices over time when the parameters
of the hedonic function may themselves
be changing over time. He finds the results of hedonic
indices to not be invariant to the choice of
reference-period characteristic vector set z. The
use of a sales (quantity) weighted average vector
of characteristics proposed by Silver (1999) is considered,
but Diewert notes that over long time periods
this may become unrepresentative. 33 Of
course, if the dummy-variable approach is used in
a chained formulation as outlined in Section C.3,
the weighted averages of characteristics remain
reasonably up to date, though chaining has its own
pros and cons (see Chapter 15). A fixed-base alternative
noted by Diewert (2003) is to use a
32 In Chapter 15, Section C.3, the issue of adjusting the
base versus the current period’s price is discussed, since
there are different data demands.
33 Other averages may be proposed—for example, the
needs of an index representative of the “typical” establishment
would be better met by a trimmed mean or median.
Laspeyres-type comparison with the base-period
parameter set, and a Paasche-type current-period
index with the current-period parameter set, and
take the geometric mean of the two indices for reasons
similar to those given in Chapter 17, Section
B.3. The resulting Fisher-type index is similar to
that given in equation (21.32) proposed by Feenstra
(1995). 34 A feature of the time dummy approach
in is that it implicitly takes a symmetric average
of the coefficients by constraining them to be
the same. But what if, as is more likely the case,
only base-period hedonic regression coefficients
are available Since hedonic indices based on a
symmetric average of the coefficients are desirable,
the spread or difference between estimates
based on either a current or a reference-period
characteristics set is an indication of potential bias,
and estimates of such spread may be undertaken
retrospectively. If the spread is large, estimates
based on the use of a single period’s characteristics
set, say the current period, should be treated with
caution. More regular updating of the hedonic regressions
is likely to reduce spread because the
periods being compared will be closer and the
characteristics of the items in the periods compared
more similar.
Weighting
21.86 OLS estimators implicitly treat each item
as being of equal importance, although some items
will have quite substantial sales, while for others
sales will be minimal. It is axiomatic that an item
with sales of more than 5,000 in a month should
not be given the same influence in the regression
estimator as one with a few transactions. Commodities
with very low sales may be at the end of
their life cycles or be custom made. Either way,
their (quality-adjusted) prices and price changes
may be unusual. 35 Such observations with unusual
prices should not be allowed to unduly influence
34 Diewert (2002c) also suggests matching items where
possible and using hedonic regressions to impute the prices
of the missing old and new ones. Different forms of
weighting systems, including superlative ones, can be applied
to this set of price data in each period for both
matched and unmatched data.
35 Such observations have higher variances of their error
terms, leading to imprecise parameter estimates. This
would argue for the use WLS estimators with quantity sold
as the weight. This is one of the standard treatments for
heteroskedastic errors (see Berndt, 1991)
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