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REVERSIBILITY TESTS/TESTS OF ADEQUACY OF INDEX NUMBERS Submitted to :Prof. S.C. Singh Submitted By :-SIDDHANT KAPOORRoll No. - 40

Reversibility Tests/ Tests of Adequacy The following tests have been suggested to select the adequacy of an index number :Time reversal testFactor reversal testCircular TestTime Reversal TestIt is used to test whether a given method will work both backwards and forwards with respect to time.For example, if P01 is a price index in the current year 1 with base of preceding year 0 and P10 is a price index for the base year 0 based on the current year 1, then the following relation should be satisfied:P01 =

orP01 * P10 = 1&Q01 * Q10 = 1

Let us see how Fishers ideal index formula satisfies the time reversal test.

P01 = ; P10 =

P01 * P10= = 1

Hence, Fishers ideal index satisfies the test.

Factor Reversal TestAccording to Fisher, Just as each formula should permit the interchange of two items without giving inconsistent result so it ought to permit interchanging the prices and quantities without giving inconsistent result, i.e. the two results multiplied together should give the true value ratio.That is, if p1 and p0 represent the prices and q1 and q0 the quantities in the current and the base periods respectively, then the price index for period 1 with base year 0 and the quantity index for period 1 with base year 0 is given byP01 * Q01 =

The factor reversal test is satisfied only by the Fishers ideal price index as shown below:

P01 = ; Q01 =

P01 * Q01 =

= =

Hence, Fishers ideal index satisfies the test.

Circular TestThis test is concerned with the measurement of price change over a period of years when the shifting of base is desirable in a circular fashion.If Pab is price index for period b with base period a ; Pbc is the price index for period c with base period b and Pca is the price index for period a with base period c, then an index is said to satisfy the circular test providedPab * Pbc * Pca = 1This test is not satisfied by most of the common formulae used in the construction of indexes including the Fishers ideal formula.Example :- Construct Fishers price index using following data and show how it satisfies the time and factor reversal tests :

Commodity2002 Quantity Price2003 Quantity PriceA20123014B13141520C12102015D86104E5856Solution :-Commodity2002

q0 p02003

q1 p1p1q0p0q0q1p1p0q1A20123014280240420360B13141520260182300210C12102015180120300200D8610432484060E585630403040Total7826301090870Fishers ideal price index

P01 = = = 1.2471

Time Reversal Test : P01 * P10 = 1

P10 = = = 0.8019

P01 * P10 = = 1

Hence, time reversal test is satisfied.

Factor Reversal Test : P01 * Q01 =

Q01 =

Thus, P01 * Q01 = =

which is the value of

Hence, factor reversal test is also satisfied.

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