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

Producer Price Index Manual
situation typically occurs when there are two
parallel markets. There may be a primary, or official,
market in which the quantities sold, and
the prices at which they are sold are subject to
government or official control, while there may
be a secondary market—a free market or unofficial
market—whose existence may or may not be
recognized officially.
7.89 There is extensive literature in economics
dealing with theory and evidence of price dispersion
and its persistence, even when quality differences
have been accounted for. The differences
can be substantial: Yoskowitz’s (2002) study for
raw water found one supplier discriminating
against a private customer, charging $500 per acre
foot (AF) while a municipality was charged $20
per AF, though there was some evidence of arbitrage
and learning. It is not the role of this Manual
to examine such theories and evidence, so readers
are referred to the following studies: Stigler (1961)
and Lach (2002) on search cost theory; Sheshinski
and Weiss (1977) and Ball and Mankiw (1994) on
menu cost theory; and Friedman (1977) and Silver
and Ioannidis (2001) on signal extraction models.
D.2 Overall Mean/Targeted Mean
Imputation
7.90 This method uses the price changes of
other products as estimates of the price changes of
the missing products. Consider a Jevons elementary
price index, that is, a geometric mean of price
relatives (Chapter 20). The prices of the missing
items in the current period, say t + 1, are imputed
by multiplying their prices in the immediately preceding
period t by the geometric mean of the price
relatives of the remaining matched items between
these two periods. The comparison is then linked
by multiplication to the price changes for previous
periods. It is the computationally most straightforward
of methods, since the estimate can be undertaken
by simply dropping the items that are missing
from both periods from the calculation. In
practice, the series is continued by including in the
database the imputed prices. It is based on the assumption
of similar price movements. A targeted
form of the method would use similar price
movements of a cell or elementary aggregate of
similar products, or be based on price changes at a
higher level of aggregation if either the lower level
had an insufficient sample size or price changes at
the higher level were judged to be more representative
of the price changes of the missing product.
7.91 In the example in Table 7.2(b) the January
to February comparison for both product types is
based on products 1, 2, 5, 6, and 8. For March
compared with January—weights all equal to
unity—the product 2 and product 6 prices are imputed
using the short-run price change for February
(p 2 ) compared with March (p 3 ) based on products
1, 5, and 8. Since different formulas are used
for elementary aggregation, the calculation for the
three main formulas are illustrated here (see Chapter
20 for choice of formulas). The geometric mean
of the price ratios—the Jevons index—is
1/3
N
2 3 ⎡ 3 2⎤
(7.7) PJ( p , p ) = ⎢ ∏ pi / pi
⎥
⎣ i=
1 ⎦
= ⎡
⎣
p / p × p / p × p / p
( 3 2 ) ( 3 2 ) ( 3 2
) ⎤
1/3
1 1 5 5 8 8
( 6/5) ( 12/11 ) ( 10/10) ⎤
1/3
= ⎡⎣ × × ⎦
= 1.0939, or a 9.39 percent increase.
The ratio of average (mean) prices—the Dutot index—is
(7.8)
N
N
2 3 3 2
D( , ) = ∑ i
/ / ∑ i
/
i= 1 i=
1
3 3 3 2 2 2
p1 p5 p8 p1 p5 p8
P p p p N p N
( ) ( )
= + + /3 ÷ + + /3
= (6 + 12 + 10) / (5 + 11 + 10) = 1.0769,
or a 7.69 percent increase.
The average (mean) of price ratios – the Carli index
- is:
N
3 2 3 2
(7.9) PC( P , P ) = ∑ ( pn / pn)/
N
n=
1
3 2 3 2 3 2
1 1 5 5 8 8
( )
= ⎡ p / p ( p / p ) ( p / p ) ⎤
⎣
+ +
⎦
/3
= [(6/5 + 12/11 + 10/10)] / 3 = 1.09697,
or a 9.697 percent increase.
7.92 In practice the imputed figure would be
entered onto the data sheet. Table 7.2(b) has the
overall mean imputation in March for product 2
and 6, using the Jevons index, as 1.0939 x 6 =
6.563 and 1.0939 x 12 = 13.127, respectively,
(bold type). It should be noted that the Dutot index
is in this instance lower that the Jevons index, a result
not expected from the relationships established
in Chapter 20. The relationship in Chapter 20 assumed
the variance in prices would increase over
time whereas in Table 7.1(b), it decreases for the
three products. The arithmetic mean of price rela-
⎦
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