The basic principles involved in constructing a price index number are:
1. A base year is selected and the prices of a group of commodities in that year are noted.
2. Prices of the selected group of commodities for the given years that are to be compared are noted.
3. The index number for the base year prices is always denoted as 100.
4. Changes in the prices of given years (current years, in statistical terms) are shown as percentage variation from the base.
Thus, the construction of an index number requires the following steps:
(i) The choice of the base year;
(ii) The choice of commodities whose prices are to be taken into account;
(iii) The collection of data, i.e., price quotations for the selected group of items in the base year and the current year;
(iv) Assigning proper weights to different items, if so desired, to remove ambiguity or bias; and
(v) Averaging the data so as to express the prices of the given years as percentage of the prices of the base year.
The statistical technique for the final step comprises various methods depending upon the availability of data, the degree of accuracy desired, and the nature of the problem under investigation. These are the simple or the weighted aggregates of actual prices, or price relative methods.
The price relative’s method is generally preferred for two reasons. First, even if there were only a single commodity being bought and sold, a price relative would most conveniently show relatives and the index number are usually written, without the decimal point, as percentages.
Secondly, the use of price relatives is all the more important when we are working with many different prices. Some items cost a few paisa, others cost thousands of rupees.
In such cases, the average of actual prices may not give a true picture of changes; for instance, a very slight change in the price of cars would outweigh any significant change in the price of cakes.
But the size of individual prices makes no difference when price relatives are used. Price relatives, thus, give an accurate picture of what has happened.
Having decided which prices to include, we compute price relatives and average them. In the case of the simple average method, we have to just add the price relatives and divide it by the number of items.
A large number of items will usually be required for constructing a general price index. The computation of such an index number is illustrated.
In the above illustration, we have assumed that all items are of equal importance. This may not be so. Thus, in order to count the differences in the importance of each item, it becomes necessary to assign weights to them. Then a weighted average of price relatives is to be computed.
Index numbers are constructed to measure the behaviour of various kinds of price averages. The most commonly used indices are of: (i) the general level of prices of all goods, services, and securities sold for money; (ii) retail prices of consumer goods; (iii) wholesale prices; and (iv) the cost of living.
Problems involved in construction of Index Numbers:
The construction of price index numbers involves a number of problems:
1. Selecting base year:
The first problem arises in the selection of the base year. The base your should be normal, i.e., prices of that year should not be subject to a boom or depression or the effect of unusual forces like wars, floods, famines, etc.
Otherwise, all the other indices that are related to such base year will present distorted facts and conclusions as a result of the abnormal conditions then prevailing.
Further, the base period should not be too far in the past since relative prices tend to change over time; the more remote in time the base period, the more likely the distortions in the index will appear in the more recent periods.
2. Selection of items:
Out of an unwieldy list of commodities required, representative items are to be selected according to the purpose and type of the index number.
In selecting items, the following points are to be considered: (i) items should be representative of the taste, habits and traditions of the people; (ii) they should be cognisable; (iii) they should be such as are not likely to vary in quality over two different periods and places; (iv) the economic and social importance of the various items of consumption should also be considered; and (u) the items must be fairly large in number, because reliability greatly depends on the adequacy of the member.
3. Data Collection:
A very important difficulty associated with the computation of index numbers is with regard to the collection of the necessary, adequate, representative and continuous data.
In most of the cases where adequate and correct information is not available due to the unorganised market and illiterate and indifferent population, the difficulty is enhanced.
The assignment of different degree of importance to different articles is known as weighting. It is necessary to come to right, unbiased conclusion regarding weights.
But the assignment of weights, which is a matter of considerable skill, is arbitrarily done.
As there are no strictly logical indicators to choose relative weights, personal judgement is bound to creep into an arbitrary decision. Thus, the result of index numbers based on such weights cannot be regarded as truly correct.
5. Economic dynamism:
In a dynamic, economy, there is a continuous change in the nature of consumption and commodities which adds to the difficulties of comparison and construction of index numbers over a period of time.
(a) Many new commodities may come into existence and the old may disappear; thus, long-run comparison may involve difficulties.
(b) The quality and quantity of the commodities may change from time to time, e.g., the quality of a 1960 model motorcar is quite different from that of a 1980 model.
(c) Income, education, fashion and other factors may change the consumption pattern of the people and indices compiled for a period of time may become non-comparable.
6. Selection of Average:
Another problem is that of employing a proper method of averaging to get an index figure. There are various methods of averaging and the use of different types of averages gives different results, thereby making comparison difficult.
However, the arithmetic mean and sometimes the geometric mean are commonly used for constructing the price indices.
Price indices are, thus, a fair indication of whether our money is buying more or less in one period in relation to another. However, there is no way to measure exactly the changes in the value of money over a period of years, even if we use a much more elaborate technique.