Despite the importance of the index numbers in studying the economic and commercial activities, and in measuring the relative changes in the price level as the economic barometers, they suffer from certain limitations for which they should be very carefully used and interpreted. The following are some of the chief limitations among others:
- They are only approximate indicators of the change of a phenomenon viz. price level, quantity level, const of living, production activity etc. They never exactly represent the changes in the relative level of a phenomenon. This is because; the index numbers are constructed mostly on the sample data.
- They are liable to be misused by a statistician with certain ulterior motive. If, purposively a wrong base year has been chosen, irrational weights have been assigned, inappropriate average has been used or irrelevant items have been included in the construction of an index number, the result would be highly misleading and fallacious.
- They are prone to embrace errors at each and every stage of construction viz.:
(i) Selection of the items and their numbers
(ii) Obtaining the price quotations
(iii) Selection of the base period
(iv) Assignment of weights
(v) Choice of the formula.
- They are liable to misrepresent the true picture of a phenomenon, if he limited number of items chosen are not representative of the universe.
- They are not capable of reflecting properly the relative changes in the quality level of the products which very much change in modern times.
- They are not capable of being used for any other purpose than the one for which they have been constructed particularly. Thus, a wholesale price index number cannot measure the cost of living, or an index number of production cannot measure productivity of a particular industry.
- There is no such formula of index number which is absolutely free from errors and limitations. Even, the Fisher’s ideal formula does not satisfy certain tests of consistency viz. circular test. Similarly, Laspeyre’s formula suffers from upward bias and Paasche’s from downward bias.