In this article we will discuss about:- 1. Meaning of Index Numbers 2. Methods of Construction of Index Number 3. Difficulties in the Construction of Index Numbers 4. Uses.
Meaning of Index Numbers:
An index number is a statistical derive to measure changes in the value of money. It is a number which represents the average price of a group of commodities at a particular time in relation to the average price of the same group of commodities at another time.
Professor Chandler defines it thus – “An index number of prices is a figure showing the height of average prices at one time relative to their height at some other time that is taken at the base period.” To understand the meaning of the term index number, three points are to be noted.
First, an average figure relates to a single group of commodities. But the various items in the group are expressed in different units. For example, a consumer price index contains such diverse items as food, clothing, fuel and lighting, house rent, and miscellaneous things. Food consists of wheat, ghee, etc. expressed in kgs. cloth is expressed in metres, and lighting in kws. An index number expresses the average of all such diverse items in different units.
Second, an index number measures the net increase or decrease of the average prices for the group under study. For instance, if the consumer price index has increased from 150 in 1982 as compared to 100 in 1980, it shows a net increase of 50 per cent in the prices of commodities included in the index.
Third, an index number measures the extent of changes in the value of money (or price level) over a period of time, given a base period. If the base period is the year 1970, we can measure change in the average price level for the preceding and succeeding years.
Methods of Construction of Index Number:
In constructing an index number, the following steps should be noted:
1. Purpose of the Index Number:
Before constructing an index number, it should be decided the purpose for which it is needed. An index number constructed for one category or purpose cannot be used for others. A cost of living index of working classes cannot be used for farmers because the items entering into their consumption will be different.
2. Selection of Commodities:
Commodities to be selected depend upon the purpose or objective of the index number to be constructed. But the number of commodities should neither be too large nor too small. Moreover, commodities to be selected must be broadly representative of the group of commodities. They should also be comparable in the sense that standard or graded items should be taken.
3. Selection of Prices:
The next step is to select the prices of these commodities. For this purpose, care should be taken to select prices from representative persons, places or journals or other sources. But they must be reliable. Prices may be quoted in money terms i.e. Rs. 100 per quantal or in quantity terms, i.e. 2 kg per rupee.
Care should be taken not to mix these prices. Then the problem is to select wholesale or retail prices. This depends on the type of index number. For a consumer price index, wholesale prices are required, for a cost of living index, retail prices are needed. But different prices should not be mixed up.
4. Selection of an Average:
Since index numbers are averages, the problem is how to select an appropriate average. The two important averages are the arithmetic mean and geometric mean. The arithmetic mean is the simpler of the two. But geometric mean is more accurate. However, the average prices should be reduced to price relatives (percentages) either on the basis of the fixed base method or the chain base method.
5. Selection of Weights:
While constructing an index number due weightage or importance should be given to the various commodities. Commodities which are more important in the consumption of consumers should be given higher weightage than other commodities. The weights are determined with reference to the relative amounts of income spent on commodities by consumers. Weights may be given in terms of value or quantity.
6. Selection of the Base Period:
The selection of the base period is the most important step in the construction of an index number. It is a period against which comparisons are made. The base period should be normal and free from any unusual events such as war, famine, earthquake, drought, boom, etc. It should not be either very recent or remote.
7. Selection of Formula:
A number of formulas have been devised to construct an index number. But the selection of an appropriate formula depends upon the availability of data and purpose of the index number. No single formula may be used for all types of index numbers.
We give below an example each of the simple price index and the weighted price index.
Simple Price Index:
To construct a simple price index, compute the price relatives and average them. Add the price relatives and divide them by the number of items. Table 1 illustrates the construction of a simple index of wholesale prices.
The preceding table shows that 1970 is the base period and 1980 is the year for which the price index has been constructed on the basis of price relatives. The index of wholesale prices in 1980 comes to 174. This means that the price level rose by 74 per cent in 1980 over 1970.
Weighted Price Index:
Taking the example of Table 1 already given, we assign high weights to commodities of greater importance to consumers and low weights to commodities of lesser importance.
The weighted price index is more accurate than the simple price index. In the example given above, the weighted price index shows an increase of 91 per cent in the price level in 1980 over 1970 as against the increase of 74 per cent according to the simple price index.
Difficulties in the Construction of Index Numbers:
There are many difficulties in the construction of index numbers.
They are discussed as under:
1. Difficulties in the Selection of the Base Period:
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.
2. Difficulties in the Selection of Commodities:
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.
3. Difficulties in the Collection of Prices:
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.
4. Arbitrary Assigning of Weights:
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.
5. Difficulty of Selecting the Method of Averaging:
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.
6. Difficulties Arising from Changes Overtime:
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.
7. Not All Purpose:
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. 0
8. International Comparisons not Possible:
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.
9. Comparisons of Different Places 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.
10. Not Applicable to an Individual:
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.
Uses of Index Numbers:
Index numbers possess much practical importance in measuring changes in the cost of living, production trends, trade, income variations, etc.
Some of the uses of index numbers are discussed below:
1. In Measuring Changes in the Value of Money:
Index number are used to measure changes in the value of money. A study of the rise or fall in the value of money is essential for determining the direction of production and employment to facilitate future payments and to know changes in the real income of different groups of people at different places and times.
As pointed out by Crowther, “By using the technical device of an index number, it is thus possible to measure changes in different aspects of the value of money, each particular aspect being relevant to a different purpose.”
2. In Cost of Living:
Cost of living index numbers in the case of different groups of workers throw light on the rise or fall in the real income of workers. It is on the basis of the study of the cost of living index that money wages are determined and dearness and other allowances are granted to workers. The cost of living index is also the basis of wage negotiations and wage contracts.
3. In Analysing Markets for Goods and Services:
Consumer price index numbers are used in analysing markets for particular kinds of goods and services. The weights assigned to different commodities like food, clothing, fuel, and lighting, house rent, etc., govern the market for such goods and services.
4. In Measuring Changes in Industrial Production:
Index numbers of industrial production measure increase or decrease in industrial production in a given year as compared to the base year. We can know from such as index number the actual condition of different industries, whether production is increasing or decreasing in them, for an industrial index number measures changes in the quantity of production.
5. In Internal Trade:
The study of indices of the wholesale prices of consumer and industrial goods and of industrial production help commerce and industry in expanding or decreasing internal trade.
6. In External Trade:
The foreign trade position of a country can be assessed on the basis of its export and import indices. These indices reveal whether the external trade of the country is increasing or decreasing.
7. In Economic Policies:
Index numbers are helpful to the state in formulating and adopting appropriate economic policies. Index numbers measure changes in such magnitudes as prices, incomes, wages, production, employment, products, exports, imports, etc.
By comparing the index numbers of these magnitudes for different periods, the government can know the present trend of economic activity and accordingly adopt price policy, foreign trade policy and general economic policies.
8. In Determining the Foreign Exchange Rate:
Index numbers of wholesale price of two countries are used to determine their rate of foreign exchange. They are the basis of the purchasing power parity theory which determines the exchange rate between two countries on inconvertible paper standard.