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

Producer Price Index Manual
Table 22.24. Lowe, Young, Geometric Laspeyres,
and Centered Rolling-Year Indices with Imputed
Prices
Year
Month P LOI P YI P GLI P CRY
1970 12 1.0000 1.0000 1.0000 1.0000
1971 1 1.0568 1.0624 1.0611 1.0091
2 1.0742 1.0836 1.0762 1.0179
3 1.1545 1.1498 1.1238 1.0242
4 1.2312 1.2334 1.2014 1.0298
5 1.3524 1.3682 1.3295 1.0388
6 1.4405 1.4464 1.4047 1.0478
7 1.3768 1.4038 1.3798 1.0547
8 1.3364 1.3789 1.3398 1.0631
9 1.1949 1.2187 1.1955 1.0729
10 1.1548 1.1670 1.1514 1.0814
11 1.1661 1.1747 1.1672 1.0885
12 1.0863 1.0972 1.0939 1.0965
1972 1 1.1426 1.1580 1.1523 1.1065
2 1.1803 1.1971 1.1888 1.1174
3 1.2544 1.2630 1.2463 1.1254
4 1.3260 1.3374 1.3143 1.1313
5 1.4306 1.4545 1.4244 1.1402
6 1.5765 1.5831 1.5423 1.1502
7 1.5273 1.5527 1.5326 1.1591
8 1.4402 1.4841 1.4444 1.1690
9 1.3034 1.3343 1.2972 1.1806
10 1.2758 1.2970 1.2675 1.1924
11 1.2875 1.3062 1.2873 1.2049
12 1.1888 1.2078 1.1981 1.2203
1973 1 1.2506 1.2791 1.2601 1.2386
2 1.3119 1.3426 1.3230 1.2608
3 1.3852 1.4106 1.3909 1.2809
4 1.4881 1.5115 1.4907 1.2966
5 1.6064 1.6410 1.6095 1.3176
6 1.8451 1.8505 1.7877 1.3406
7 1.7679 1.7981 1.7684 0.0000
8 1.6773 1.7263 1.6743 0.0000
9 1.5271 1.5700 1.5090 0.0000
10 1.5410 1.5792 1.5195 0.0000
11 1.5715 1.6075 1.5613 0.0000
12 1.4307 1.4651 1.4359 0.0000
[p 1 0 ,…,p 5 0 ] where the nth price in this vector is defined
as
(22.33)
p
0
n
≡
12
0, m 0, m
∑ pn
qn
m=
1
12
0, m
∑ qn
m=
1
; n = 1,…,5.
The Rothwell price index for month m in year t can
now be defined as follows:
0 tm , 0. m
(22.34) PR
( p , p , q )
m = 1,…,12.
≡
5
∑
n=
1
5
∑
n=
1
p
q
tm , 0, m
n n
pq
0 0. m
n n
Thus, as the month changes, the quantity weights
for the index change. The month-to-month movements
in this index, therefore, are a mixture of
price and quantity changes. 47
22.88 Using the modified Turvey data set, the
base year is chosen to be 1970 as usual, and the index
is started off at December of 1970. The Rothwell
index P R is compared to the Lowe index with
carryforward of missing prices P LO in Table 22.25.
To make the series a bit more comparable, the
normalized Rothwell index P NR is also listed in Table
22.25; this index is simply equal to the original
Rothwell index divided by its first observation.
22.89 Viewing Figure 22.6, which plots the
Lowe index with the carryforward of the last price
and the normalized Rothwell index, it is clear that
the Rothwell index has smaller seasonal movements
than the Lowe index and is less volatile in
general. 48 However, it is evident that there still are
large seasonal movements in the Rothwell index
and it may not be a suitable index, for measuring
general inflation without some sort of seasonal ad-
;
index. 46 This index makes use of seasonal baskets
in the base year, denoted as the vectors q 0,m for the
months m = 1, 2,…,12. The index also makes use
of a vector of base year unit-value prices, p 0 ≡
46 This is the index favored by Baldwin (1990, p. 271) and
many other price statisticians in the context of seasonal
products.
47 Rothwell (1958, p. 72) showed that the month-to-month
movements in the index have the form of an expenditure ratio
divided by a quantity index.
48 For all 37 observations in Table 22.25, the Lowe index
has a mean of 1.3465 and a standard deviation of 0.20313,
while the normalized Rothwell has a mean of 1.2677 and a
standard deviation of 0.18271.
584