Consistency of index no

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1. TEST OF CONSISTENCY OF INDEX NUMBERS PRESENTED BY: ANKIT AGRAWAL 16MBA(FM)025

2. TESTS TO CHECK CONSISTENCY OF INDEX NUMBER Order reversal test Time reversal test Factor reversal test Circular test Unit test

3. ORDER REVERSAL TEST This test requires that a formula of Index number should be such that the value of the index number remains the same, even if, the order of arrangement of the items is reversed, or altered. This test is satisfied by all methods of index number.

4. TIME REVERSAL TEST This test requires that the formula of index number should be such that it turns the value of the index number to its reciprocal when the time subscripts of the formula are reversed and the product of both results to unity.

5. In order to satisfy this test index formula must prove the following equation:   P 01   x  P 10  = 1 Except Laspeyre and Paasche all index formula passes this test.

6. METHOD ORIGINAL FORM REVERSE FORM PRODUCT OF THE TWO CHECK FOR TIME REVERSAL TEST

7. FACTOR REVERSAL TEST This test proposes that a formula of index number should be such that it permits the interchange of the price and the quantity factors without giving inconsistent result.

8. For the Factor Reversal test, a formula of index number should satisfy the following equation: Price index × Quantity Index = Value Index i.e.   P 01  x Q 01 =  ∑ p 1 q 1 /p q Only fisher formula of index number passes this test.

9. METHOD ORIGINAL FORM REVERSED FORM PRODUCT OF THE TWO CHECK FOR FACTOR REVERSAL TEST

10. CIRCULAR TEST This test requires that an index number formula should be such that it works in a circular fashion. This test is based on the shiftability of base period.

11. A formula to satisfy the test should comply with the following equation:       P ab  × P bc  × P ca  = 1. (for three periods a,b and c) This test is satisfied by only kelley’s method.

12. METHOD P O1 P 12 P 20 P 01 *P 12 *P 20 CHECK FOR CIRCULR TEST

13. UNIT TEST This test requires that an index number formula should be such that it does not affect the value of the index number, even if, the units of the price or quantities quoted are altered. This test is satisfied by all the index formula.

14. THANK YOU