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

22. Treatment of Seasonal Products
Figure 22.2. Rolling-Year Approximate Laspeyres, Paasche, and Fisher Price Indices
1.4
Index
1.3
1.2
1.1
Pal AL
(fixed)
Pap AP
(fixed)
Paf AF
(fixed)
PPal AL
(chain)
Pap PAP
(chain)
Paf (chain)
P (chain)
AF
1.0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
Months
22.60 P SAARY equals the approximate rolling-year
index P ARY multiplied by the seasonal adjustment
factor SAF, which in turn is equal to the rollingyear
Laspeyres index P LRY divided by P ARY . However,
starting at December of 1972, the rollingyear
index P LRY differs from the corresponding
seasonally adjusted approximate rolling-year index
P SAARY . It is apparent that for these last 13 months,
P SAARY is surprisingly close to P LRY . 23 P LRY , P SAARY
and P ARY are graphed in Figure 22.3. Due to the acceleration
in the monthly inflation rate for the last
year of data, it can be seen that the seasonally adjusted
approximate rolling-year series, P SAARY , does
not pick up this accelerated inflation rate for the
first few months of the last year (it lies well below
P LRY for February and March of 1973), but in general,
it predicts the corresponding centered year
quite well.
23 The means for the last 13 observations in columns 1
and 2 of Table 22.20 are 1.2980 and 1.2930. A regression
of P L on P SAARY leads to an R 2 of 0.9662 with an estimated
variance of the residual of .000214.
22.61 The above results for the modified Turvey
data set are quite encouraging. If these results can
be replicated for other data sets, statistical agencies
will be able to use the latest information on
year-over-year monthly inflation to predict reasonably
well the (seasonally adjusted) rolling-year
inflation rate for a rolling-year that is centered
around the last two months. Thus, policymakers
and other interested users of the PPI could obtain a
reasonably accurate forecast of trend inflation
(centered around the current month) some six
months in advance of the final estimates.
22.62 The method of seasonal adjustment used
in this section is rather crude compared to some of
the sophisticated econometric or statistical methods
that are available. These more sophisticated
methods could be used to improve the forecasts of
trend inflation. However, it should be noted that if
improved forecasting methods are used, it will be
useful to use the rolling-year indices as targets for
the forecasts rather than using a statistical package
that simultaneously seasonally adjusts current data
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