There are many difficulties faced in the construction of index numbers. They are discussed as under:
The first difficulty relates to the selection of the base year. The base year should be normal. But it is difficult to determine a truly normal year. Moreover, what may be the normal year today may become an abnormal year after some period. Therefore, it is not advisable to have the same year as the base period for a number of years. Rather, it should be changed after ten years or so. But there is no fixed rule for this.
The selection of representative commodities for the index number is another difficulty. The choice of representative commodities is not an easy matter. They have to be selected from a wide range of commodities which the majority of people consume. Again, what were representative commodities some ten years ago may not be representative today. The consumption pattern of consumers might change and thereby make the index number useless. So the choice of representative commodities presents real difficulties.
Another difficulty is that of collecting adequate and accurate prices. It is often not possible to get them from the same source or place. Further, the problem of choice between wholesale and retail prices arises. There are much variations in the retail prices. Therefore, index numbers are based on wholesale prices.
In calculating weighted price index, a number of difficulties arise. The problem is to give different weights to commodities. The selection of higher weight for one commodity and a lower weight for another is simply arbitrary. There is no set rule and it entirely depends on the investigator. Moreover, the same commodity may have different importance for different consumers. The importance of commodities also changes with the change in the tastes and incomes of consumers and also with the passage of time. Therefore, weights are to be revised from time to time and not fixed arbitrarily.
Another difficulty is to select an appropriate method of calculating averages. There are a number of methods which can be used for this purpose. But all methods give different results from one another. It is, therefore, difficult to decide which method to choose.
In the present times, changes in the nature of commodities are taking place continuously overtime due to technological changes. As a result, new commodities are introduced and people start consuming them in place of the old ones. Moreover, prices of commodities might also change with technical changes. They may fall. But new commodities are not entered into the list of commodities in preparing the index numbers. This makes the index numbers based on old commodities unreal.
An index number constructed for a particular purpose cannot be used for some other purpose. For instance, a cost of living index number for industrial workers cannot be used to measure the cost of living of agricultural workers. Thus there are no all purpose index numbers.
International price comparisons are not possible with index numbers. The commodities consumed and included in the construction of an index number differ from country to country. For instance, meat, eggs, cars, and electrical appliance are included in the price index of advanced countries whereas they are not included in that of backward countries. Similarly, weights assigned to commodities are also different. Thus international comparisons of index numbers are not possible.
Even if different places within a country are taken, it is not possible to apply the same index number to them. This is because of differences in the consumption habits of people. People living in the northern region consume different commodities than those consumed by the people in the south of India. It is, therefore, not right to apply the same index number to both.
An index number is not applicable to an individual belonging to a group for which it is constructed. If an index number shows a rise in the price level, an individual may not be affected by it. This is because an index number reflects averages.
It may be concluded from the difficulties and limitations of index numbers that index numbers are at best approximations to measure changes in the value of money. However, these difficulties become less significant if index numbers are constructed for short intervals. This is because habits, tastes, techniques of production and the qualities of commodities entering into a price index number do not change during the short period.