The following points highlight the seven major problems of index numbers. The problems are: 1. Inadequate Coverage 2. Choice of Weights 3. Choice of Base Year 4. Inaccuracy 5. Income Variation 6. The Time Factor 7. Comparability.
Problem # 1. Inadequate Coverage:
The first problem lies in the fact that it is impossible to cover all commodities and their price. Moreover, the price at which a particular good or service is sold may vary from one part of the market to another. A representative selection has to be made, therefore, and a further complication will arise when choices have to be made among various grades or qualities of goods.
Problem # 2. Choice of Weights:
Secondly, it is necessary to decide how much significance or relative weight should be given to the items selected. Since consumers’ incomes and tastes differ the pattern of expenditure will differ from one locality to another and from one period to another.
In practice, the complier of the index number makes an arbitrary decision by selecting for a particular year (the base year) what is considered to be the pattern of expenditure (known as a ‘basket’) in a sample of consumers.
A relative weight is allocated to each item according to its share of total expenditure. The pattern selected is used to apply weights to the various commodities in succeeding years for which the index number is calculated.
Clearly, the index will be limited in its significance. There will be many consumers who will put different weights to their expenditure by buying different baskets of goods.
A further drawback is that the chosen basket is really only applicable to the base year. Over a period of time, the whole pattern of expenditure changes as incomes alter, as the national income changes in size and in the manner of its distribution, as qualities alter, and as new commodities and services come into existence and use.
These are inherent defects-weighted index numbers. The selection of weights is arbitrary and based upon the personal inclinations of the statistician. Even if weighting is based upon relative consumption, the final figures are only approximations because no two families spend in an identical manner.
Problem # 3. Choice of Base Year:
The third major problem concerns the choice of a base year. Movements in prices will appear to be more or less significant, according to the base year chosen for the prices of items selected. It is important, therefore, to select a base year when prices were relatively stable and so years during periods either of severe inflation or deflation should be avoided.
This problem arises because the Retail Price Index can equally be calculated as a base-weighted or a current-weighted index, but the two types of index do not necessarily give the same answer. For instance, consider a simple example of two goods X and Y which have the following prices and quantities purchased in the base year 1 and the current year 2.
The current-weighted index is given by:
Year 2 = (8p × 6) + (25p × 1)/10p × 6) + (20p × 1) = 73/80 = 0.91. (Year 1 = 100)
The base-weighted index is given by:
Year 2 = (8p × 5) + (25p x 5) / (10p × 5) + (20p × 5) = 165/150 =1.10. (Year 1 = 100)
According to the base-weighted index, the general level of prices rose in year 2 compared with year 1 (by 10 per cent), but according to the current- weighted index, prices fell in year 2 (by 0 per cent). The problem of choice is that if base weights are not updated, items will continue to be included that are no longer relevant in household expenditure. On the other hand, changing weights in order to keep them current could lead to the index being influenced by changes in quantities and therefore not be properly representative of price movements only.
Problem # 4. Inaccuracy:
Statistics are not always accurate. Index numbers based on false statistics may mislead us.
Problem # 5. Income Variation:
Cost of living index numbers suffer from another defect. Incomes vary widely and different income groups have different consumption habits. Even within the same income level there are different groups among whom the items consumed and their relative importance vary widely. So, there ought to be as many different cost of living index numbers as there are groups within the community. In practice it would be difficult to construct so many index numbers.
Problem # 6. The Time Factor:
No inferences should be drawn by comparing index numbers of years separated by a long period of time. The uniformity of bases essential for comparison between different years may not exist. Consumption habits and standards of living change in course of time. Methods of production and the type of goods produced do not remain the same.
New commodities come into existence and old commodities disappear. These factors might be ignored in the short period. But long-run comparisons (e.g., between 1898 and 1998) may be thoroughly misleading.
Problem # 7. Comparability:
Index numbers of different places are hardly comparable. The significance of prices to consumption varies according to taste, habits, climate, etc. The cost of living index number of London will include coal prices as an important item. In Calcutta and Bombay they are not important. Hence, a comparison of the cost indices of these places is meaningless.
On account of the various difficulties associated with their construction, little importance can be attached to index numbers for comparing price changes over long periods of time. The further from the base year, the more inaccurate is the index number likely to become, for the basket is more liable to change.
Moreover, since patterns of expenditure vary in different localities and different countries, an index number has very limited value in comparing price changes in different places.
Nevertheless, despite its limitations, an index number is the best means of measuring short-term changes in the level of prices of the particular group of commodities selected. So the conclusion is : index numbers are very useful when used properly but can make little sense if used in ignorance of their true meaning.