Tests of Adequacy of Index Number Formulae

Several formulae have been suggested for constructing index numbers and the problem is that of selecting the most appropriate one in a given situation. The following tests are suggested for choosing an appropriate index:

1.    Unit Test.

The unit test requires that the formula constructing an index should be independent of the units in which, or for which, prices and quantities are quoted.

2.    Time Reversal Test

Prof. Irving fisher has made a Careful study of the various proposals for computing index numbers and has suggested various tests to be applied to any formula to indicate whether or not it is satisfactory. The two most important of these he calls the time reversal test and the factor reversal test.

3.    Factor Reversal Test.

Another test suggested by Fisher is known as 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 word of Fisher, “Just as each Formula should permit the interchange of the two lines without giving inconsistent results. So it ought to permit interchange the prices and quantities without giving inconsistent result, i.e., the two results multiplied together should give the true value ratio.”

4.    Circular Test

Another test of the adequacy of index number formula is what s known as ‘circular test’. If in the use of index numbers interest attaches not merely to a comparison of two years, but to the measurement of price changes over a period of years.

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