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Fisher’s Ideal Index

Prof. Irving Fisher has given a number of formulae for constructing index numbers and of these he calls one as the ‘ideal’ index. The Fisher’s Ideal Index is given by the formula:
Fisher method

It shall be clear from the above formula that Fisher’s Ideal Index is the geometric mean of the Laspeyres and Paasce indices. Thus in the Fisher’s method we average geomatrcally formulae that err in opposite directions.

The above formula is known as ‘Ideal’ because of the following reasons:

(i)    It is based on the geometric mean which is theoretically considered to be the best average for constructing index numbers.

(ii)    It takes into account both current year as well as base year prices and quantities.

(iii)    It satisfies both the time reversal test as well as the factor reversal test as suggested by Fisher.

(iv)    It is free bias. The two formulae (Laspeyres and Paasche’s) that embody the opposing type and weighted biases are, in the ideal formula, crossed geometrically, i.e., by an averaging process that of itself has no bias. The result is the complete cancellation of biases of the kinds revealed by time reversal and factor reversal tests.

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