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

7. Treatment of Quality Change
to an implicit quality adjustment comparing
the price of the replacement product with the
imputed price of the discontinued one.
• Approach 2: A replacement product may be
selected, comparable in quality to the missing
product, and its price used directly to form a
price relative.
• Approach 3: The replacement may be deemed
noncomparable with the missing product, but
prices of both the missing and replacement
products may be available in an overlap period
before the product was missing. Compilers use
the price difference in this overlap period to
quality-adjust the replacement product’s price
until there are at least two observations on the
replacement product.
• Approach 4: The price of a noncomparable replacement
may be used with an explicit adjustment
for the quality difference to extract
the pure price change.
7.16 In most instances, compilers make an adjustment
to the price (price change) of the replacement
product to remove that part because of
quality differences from the product it replaces.
(This presumes the compiler has a basis for deciding
which old product a new product replaces.
More often, the change is for the outputs of a given
establishment and the choice considered obvious.)
The quality adjustment is a coefficient multiplied
by the price of the replacement product to make it
commensurate, from the producer’s point of view,
with the price of the original.
7.17 The simplest example of adjusting for
quality change is handling the variety of package
sizes encountered in all price indices. Suppose that
the size of the missing product and its replacement
differ, where quantity k of the replacement sells for
the same price in the current month as quantity j of
the original in the previous month. The conventional
matched models approach (approach 1) is
equivalent to imputing the price change of the index
of matched models in the elementary aggregate
to the unmatched models. Approach 2 would
amount to finding another instance of the product
of the same size with all other characteristics the
same and directly comparing the two prices by
forming the ratio of the price of the replacement
product with the price of the missing product in the
previous month. There is no overlap price in this
example, precluding application of approach 3.
7.18 Alternatively, the compiler can undertake
a range of explicit quality adjustments (approach
4). Suppose one package of the original contains j
units of the replacement while the replacement
package contains k units. To make the price of one
unit of the replacement commensurate with the
price of one unit of the original, it must be multiplied
by j/k, the quality adjustment. If j = 2 and k =
3, the required quality adjustment to be applied to
the price of the replacement product is 2/3. Suppose
a package of the replacement actually sells in
the current month at the same price as a package of
the original in the previous month. The price of the
replacement, after adjusting for the change in quality,
is only 2/3 that of the price of the original. If
one unit of the replacement sells for twice the price
of the original, then the quality-adjusted price is
4/3 (2 × 2/3) that of the original: the price increase
is 33 percent, not 100 percent.
7.19 The critical assumption in this explicit adjustment
by the quantity in the package is that
there is no difference in inputs between the different
package sizes. If packaging and marketing use
inputs, for example, or there are other input requirements
in providing the different package
sizes, the simple proportional adjustment by package
size will not be correct. There are two options.
If the compiler somehow knows the unit cost of
producing the two package sizes of product
through interviewing the establishment representative,
he or she can divide the price ratio of the new
package size to the old by the ratio of the unit cost
of the new package size to the old package size.
This illustrates the so-called resource cost adjustment
for quality differences.
7.20 In the final type of explicit approach, the
compiler collects data on the range of sizes available
in the market of an otherwise identical product
in the current month and estimates a linear or
log linear regression of price on package size.
Price = a+ b×
Package size
7.21 This is the so-called hedonic method. If
the intercept or constant a is zero, this would confirm
the validity of our first unit value approach to
correcting for package size. If a assumes a value
different from 0, however, he or she could impute
the value of the old size in the current month by
evaluating the estimated regression equation at the
old size. The price relative for the old item in the
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