Page 258 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes The test is not satisfied by any of the Laspeyre’s, Paasche’s or Fisher’s Method. However, the simple
aggregative method and the fixed weight aggregative method (Kelly’s method) satisfy this test.
Example 1: Compute Fisher’s ideal number and prove that it satisfies factor reversal and time
reversal test.
Price Quantity
Commodity
2002 2003 2002 2003

A 10 12 12 15
B 7 5 15 20
C 5 9 24 20
D 16 14 5 5
Solution:

Commodity Price Quantity
Item 2002 2003 2002 2003 p q p q p q p q
nn
00
n0
0n
A 10 12 12 15 144 120 180 150
B 7 5 15 20 75 105 100 140
C 5 9 24 20 216 120 180 100
D 16 14 5 5 70 80 70 80

Total ∑ pq ∑ pq ∑ pq ∑ pq
nn
0n
00
n0
505 425 530 470
Fisher’s price index
∑ pq ∑ pq
n0
n n
F
F p = P on = ∑ pq ⋅ ∑ pq × 100
0 n
00
505 530
= × × 100
425 470
= 1.188 1.128 100× ×
= 115.8
(i) Time reversal test

∑ 0n ∑ p q p q
0 0
P no = ∑ nn ⋅ ∑ p q p q
n 0
470 525
= ×
530 505

505 530 470 429
⋅
⋅
⋅
∴ P no × P on = 425 470 530 505
= 1 = 1

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