bus-stat-book1

056 1067 100 1127 100 1062 100 1062 time reversal

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Unformatted text preview: re is said to be a time bias is the method. Fisher’ s ideal index satisfies the time reversal test. Σp1 q 0 Σp1q1 P01 = × Σp 0 q 0 Σp 0 q1 P10 = Σp 0 q1 Σp 0 q 0 × Σp1q1 Σp1q 0 Then P01 × P10 = Σp1 q 0 Σp1q1 Σp0 q1 Σp0 q0 × × × Σp 0 q 0 Σp 0 q1 Σp1q1 Σp1q 0 255 = 1 =1 Therefore Fisher ideal index satisfies the time reversal test. 3. Factor Reversal test: Another test suggested by Fisher is known s factor reversal test. It holds that the product of a price index and the quantity index should be equal to the corresponding value index. In the words of Fisher, “Just as each formula should permit the interchange of the two times without giving inconsistent results, so it ought to permit interchanging the prices and quantities without giving inconsistent result, ie, the two results multiplied together should give the true value ratio. In other word, if P01 represent the changes in price in the current year and Q01 represent the changes in quantity in the current year, then Σp1q1 P01 × Q01 = Σp 0 q 0 Thus based on this test, if the product is not equal to the value ratio, there is an error in one or both of the index number. The Factor reversal test is satisfied by the Fisher’ s ideal index. Σp1 q 0 Σp1q1 ie. P01 = × Σp 0 q 0 Σp 0 q1 Q01 = Then P01 × Q01 = = = Σq1 p0 Σq1 p1 × Σq 0 p 0 Σq 0 p1 Σp1q 0 Σp1q1 Σq1 p0 Σq1p1 × × × Σp 0 q 0 Σp 0 q1 Σq 0 p 0 Σq 0 p1 Σp1q1 Σp 0 q 0 2 Σp1q1 Σp 0 q 0 256 Σp1q1 , the factor reversal test is satisfied by Σp 0 q 0 the Fisher’ s ideal index. Example 8: Construct Fisher’ s ideal index for the Following data. Test whether it satisfies time reversal test and factor reversal test. Base year Current year Commodity Quantity Price Quantity Price A 12 10 15 12 B 15 7 20 5 C 5 5 8 9 Solution: Commodity q0 p0 q1 p1 P0q0 p0q1 p1q0 p1q1 A 12 10 15 12 120 150 144 180 B 15 7 20 5 105 140 75 100 C 5 5 8 9 25 40 45 72 250 330 264 352 Since P01 × Q01 = Fisher ideal index number P01F = = = Σp1q 0 Σp1q1 × Σp0 q 0 Σp0 q1 × 100 264 352 × × 100 250 330 (1.056) × (1.067) × 100...
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