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

22. Treatment of Seasonal Products
the resultant 12 year-over-year monthly chained
Laspeyres, Paasche, and Fisher indices, P L , P P and
P F , where the month-to-month links are defined by
equations (22.4)–(22.6), are listed in Tables 22.8 to
22.10.
22.32 Comparing the entries in Tables 22.8 and
22.9, it can be seen that the year-over-year
monthly chained Laspeyres and Paasche price indices
have smaller differences than the corresponding
fixed-base Laspeyres and Paasche price indices
in Tables 22.3 and 22.4. This is a typical pattern
that was found in Chapter 19: the use of chained
indices tends to reduce the spread between
Paasche and Laspeyres indices compared to their
fixed-base counterparts. The largest percentage
difference between corresponding entries for the
chained Laspeyres and Paasche indices in Tables
22.8 and 22.9 is 4.1 percent for month 10 in 1973
(1.3593/1.3059 = 1.041). Recall that the fixed-base
Laspeyres and Paasche indices differed by 12.5
percent for the same month so that chaining does
tend to reduce the spread between these two
equally plausible indices.
22.33 The chained year-over-year Fisher indices
listed in Table 22.10 are regarded as the best esti-
Table 22.10. Year-over-Year Monthly Chained Fisher Indices
Month 1 2 3 4 5 6 7 8 9 10 11 12
1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
1971 1.1080 1.1069 1.1474 1.1487 1.1137 1.0835 1.1089 1.0741 1.0453 1.0831 1.1251 1.0837
1972 1.2048 1.2438 1.3052 1.2780 1.2114 1.1701 1.2343 1.1660 1.0886 1.1555 1.2405 1.1926
1973 1.3258 1.4027 1.4942 1.4906 1.3937 1.3378 1.4500 1.3728 1.2181 1.3323 1.4978 1.4368
Table 22.11. Year-over-Year Monthly Approximate Chained Laspeyres Indices
Month 1 2 3 4 5 6 7 8 9 10 11 12
1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
1971 1.1085 1.1068 1.1476 1.1488 1.1159 1.0844 1.1103 1.0783 1.0492 1.0901 1.1284 1.0849
1972 1.2056 1.2440 1.3057 1.2778 1.2168 1.1712 1.2346 1.1770 1.0989 1.1692 1.2482 1.1939
1973 1.3255 1.4007 1.4945 1.4902 1.4054 1.3390 1.4491 1.4021 1.2429 1.3611 1.5173 1.4417
Table 22.12. Year-over-Year Monthly Approximate Chained Paasche Indices
Month 1 2 3 4 5 6 7 8 9 10 11 12
1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
1971 1.1077 1.1057 1.1468 1.1478 1.1135 1.0818 1.1062 1.0721 1.0426 1.0760 1.1209 1.0813
1972 1.2033 1.2424 1.3043 1.2764 1.2130 1.1664 1.2287 1.1638 1.0858 1.1438 1.2328 1.1886
1973 1.3206 1.3971 1.4914 1.4880 1.3993 1.3309 1.4386 1.3674 1.2183 1.3111 1.4839 1.4300
563