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

Producer Price Index Manual
Table 9.9. Calculation of a Chained Index Using Linking Coefficients
Index 1998 Nov 02 Dec 02 Jan 03 Feb 03 Mar 03
Elementary price indices (1998 = 100)
Weight
1998
Linking Coefficient
A 0.20 100.00 120.00 121.00 1.2100 121.00 121.00 123.42
B 0.25 100.00 115.00 117.00 1.1700 119.34 120.51 121.68
C 0.15 100.00 132.00 133.00 1.3300 130.34 130.34 129.01
D 0.10 100.00 142.00 143.00 1.4300 144.43 148.72 148.72
E 0.30 100.00 110.00 124.00 1.2400 127.72 130.20 131.44
Total 100.00 119.75 124.90 1.2490 126.39 127.99 129.07
Higher-level indices (1998 = 100)
G = A+B+C 0.60 100.00 120.92 122.33 1.2233 122.78 123.22 124.56
H = D+E 0.40 100.00 118.00 128.75 1.2875 131.58 134.67 135.45
Total 100.00 119.75 124.90 1.2490 126.39 127.99 129.07
Elementary price indices (December 2002 = 100)
Linking Coefficient
1998 Nov 02 Dec 02 2000 Weight
Index
Jan 03 Feb 03 Mar 03
A 0.82645 82.65 99.17 100.00 0.25 100.00 100.00 102.00
B 0.85470 85.47 98.29 100.00 0.20 102.00 103.00 104.00
C 0.75188 75.12 99.25 100.00 0.10 98.00 98.00 97.00
D 0.69993 69.99 99.39 100.00 0.18 101.00 104.00 104.00
E 0.80645 80.65 88.71 100.00 0.27 103.00 105.00 106.00
Total 0.80064 80.06 95.88 100.00 101.19 102.47 103.34
Higher-level indices (2000 = 100)
G = A+B+C 0.81746 81.75 98.85 122.33 0.55 100.36 100.73 101.82
H = D+E 0.77670 77.67 91.65 128.75 0.45 102.20 104.60 105.20
Total 0.80064 80.06 95.88 124.90 101.19 102.47 103.34
C.7.3 Chaining indices using linking
coefficients
9.117 Table 9.9 presents an example of chaining
indices on new weights to the old reference period
(1998 = 100). The linking can be done several
ways. As described above, one can take the current
index on the new weights and multiply it by the old
index level in the overlap month (December 2002).
Alternatively, a linking coefficient can be calculated
between the old and new series during the
overlap period and this coefficient applied to the
new index series to bring the index up to the level
of the old series. The linking coefficient for keeping
the old price reference period is the ratio of the old
index in the overlap period to the new index for the
same period. For example, the coefficient for the
Total index is (124.90 ÷ 100.00) = 1.2490. This
coefficient is then applied to the Total index each
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