Which index number is called ideal index number ?

Question

Accepted Answer

The correct option is 3:
Fisher's Index number is widely regarded as the "ideal index number" in statistical analysis because it satisfies two important tests of consistency: the Time Reversal Test and the Factor Reversal Test. The Time Reversal Test requires that the index calculated forward in time should be the reciprocal of the index calculated backward in time, ensuring chronological symmetry. The Factor Reversal Test ensures that the product of the price index and the quantity index equals the value index, meaning the index correctly measures changes in both price and quantity between the two periods. Mathematically, Fisher's Index is the geometric mean of Laspeyre's Index and Paasche's Index, which helps it balance the upward bias inherent in Laspeyre's index (due to using base year quantities) and the downward bias inherent in Paasche's index (due to using current year quantities). This geometric averaging provides a result that is superior in theoretical construction and accuracy.

The incorrect option is 1:
Laspeyre's Index number uses base year quantities as weights. While simple to calculate and useful for comparison over time, it tends to overstate the price rise (exhibit an upward bias) because it ignores the substitution effect where consumers shift away from goods that have become relatively more expensive.

The incorrect option is 2:
Paasche's Index number uses current year quantities as weights. This index number tends to understate the price rise (exhibit a downward bias) because it reflects the current consumption pattern where substitution has already occurred. It also violates the Time Reversal Test, making it theoretically inconsistent.

The incorrect option is 4:
Bowley's Index number is the arithmetic mean of Laspeyre's Index and Paasche's Index. While it attempts to average out the biases, using an arithmetic mean rather than a geometric mean means it does not satisfy the critical Factor Reversal Test. Therefore, it is considered less theoretically sound than the Fisher's Index.