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

19. Price Indices Using an Artificial Data Set
Table 19.19. Quantity Data for the Service Sector
t
1 30 10 40 10 45 5 3 6 22 6 8 –28 –7 –20 –26 –36
2 28 8 39 13 47 6 2 4 19 5 9 –20 –9 –16 –23 –35
3 30 11 38 30 50 8 3 5 22 5 10 –29 –21 –20 –26 –34
4 32 14 39 60 56 13 3 6 23 5 11 –35 –42 –23 –27 –35
5 29 12 40 100 65 25 3 5 21 5 11 –30 –70 –19 –25 –36
q 1
S
q 2
S
q 3
S
q 4
S
q 5
S
q 6
S
q 7
S
q 8
S
q 9
S
q 10
S
q 11
S
q 12
S
q 13
S
q 14
S
q 15
S
q 16
S
Table 19.20. Agriculture Sector Fixed-Base Laspeyres, Paasche, Fisher, and Törnqvist Value-Added
Deflators
Period t
1 1.0000 1.0000 1.0000 1.0000
2 1.1455 1.2400 1.1918 1.2000
3 0.9636 0.9750 0.9693 0.9679
4 0.3273 0.3857 0.3553 0.3472
5 0.7545 0.7636 0.7591 0.7478
P L
t
P P
t
P F
t
P T
t
Table 19.21. Agriculture Sector Chained Laspeyres, Paasche, Fisher, and Törnqvist Price Value-
Added Deflators
Period t
1 1.0000 1.0000 1.0000 1.0000
2 1.1455 1.2400 1.1918 1.2000
3 0.9238 0.9803 0.9516 0.9579
4 0.3395 0.3808 0.3596 0.3584
5 0.7104 0.8646 0.7837 0.7758
P L
t
P P
t
P F
t
P T
t
The five intermediate inputs into the services sector
are listed as follows:
• Commodity 12 is imports of energy into the
economy;
• Commodity 13 is imports of high-technology
manufactures into the economy;
• Commodity 14 is deliveries of agricultural
output to services;
• Commodity 15 is deliveries of processed food
from manufacturing to services; and
• Commodity 16 is deliveries of traditional
manufacturing to services.
These prices and quantities are denoted by p St n and
q St n for n = 1,...,16 and t = 1,...,5. Note that q St 1 to
St
q 11 are positive (because these commodities are
outputs) and q St 12 to q St 16 are negative (since these
commodities in the services sector are intermediate
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