Index Numbers

Management > Managerial Statistics > Introduction to Index Numbers

According to the Spiegel: “An index number is a statistical measure, designed to measure changes in a variable, or a group of related variables with respect to time, geographical location or other characteristics such as income, profession, etc.”

According to Patternson: “In its simplest form, an index number is the ratio of two index numbers expressed as a percent. An index is a statistical measure, a measure designed to show changes in one variable or a group of related variables over time, with respect to geographical location or other characteristics”.

According to Tuttle: “Index number is a single ratio (or a percentage) which measures the combined change of several variables between two different times, places or situations”.

Index numbers is a statistical tool for measuring relative change in a group of related variables over two or more different times. Index number expresses the relative change in price, quantity, or value compared to a base period. An index number is used to measure changes in prices paid for raw materials; numbers of employees and customers, annual income and profits, etc.

Thus index numbers are economic barometers to judge the inflation (increase in prices) or deflationary (decrease in prices) tendencies of the economy. They help the government in adjusting its policies in case of inflationary situations.

Types of Index Numbers:

Three are three types of principal indices. They are: 1. the price index, 2. the quantity index 3. the value index.

Price Index:

It is the most frequently used form of index numbers. A price index compares charges in the price of commodities over a period. If an attempt is being made to compare the prices of the particular commodity this year to the prices of edible oils last year, it involves, firstly, a comparison of two price situations over time and secondly, the heterogeneity of the commodity given the various varieties of the commodity. The Whole Price Index (WPI). Consumer Price Index (CPI) are some of the popularly used price indices.

Quantity Index:

A quantity index measures the changes in quantity from one period to another. If in the above example, instead of the price of the commodity, we are interested in the quantum of production or consumption of the commodity in those years, then we are comparing quantities in two different years or over a period of time. The index of industrial production (IIP) is a commonly used quantity index.

Value Index:

The value index is a combination index. It combines price and quantity changes to present a more spatial comparison. The value index as such measures changes in net monetary worth. Though the value index enables comparison of the value of a commodity in a year to the value of that commodity in a base year, it has limited use. Generally, the value index is used in sales, inventories, foreign trade, etc.

Characteristics of Index Number:

Expressed in Number:

Index numbers are expressed in terms of numbers to show the extent of relative change· in price, output, consumption, etc.

Expressed as Percentage:

Index numbers are expressed in terms of percentage to show the extent of relative change· in price, output, consumption, etc. the % sign is not used.

Measures Relative Changes:

Index numbers measure the relative change in the value of a variable or a group of related variables over a period of time or between places.

Measures Changes which are not Directly Measurable:

Index numbers measures changes which are not directly measurable. The cost of living, the price level or the business activity in a country are not directly measurable but it is possible to study relative changes in these activities by measuring the changes in the values of variables/factors which effect these activities.

Expressed on an Average:

Index number presents the changes on an average bases. These are generally used to express the changes in a group of variables and not of a particular variable or commodity, if the prices of some commodities are increasing there may be at constant level. But on an average what other is j the change in prices of a group of items will be represented by index numbers. Index numbers are of special type of average.

They are Specified Averages:

Index numbers represent special case of averages, as in case of weighted averages.

They Has Universal Utility:

Generally index numbers are used to measure the changes in prices in the group of items but the changes in the quantity of agricultural production, industrial production, imports, and exports can also be measured through index numbers.

Advantages of Index Number

Used for the measurement of change in the price level or the value of money: 

Index number helps to measure the quantitative changes in variables by comparing the data of current year with the data of base year. Hence the index number can be used to know the impact of the change in the value of money on different sections of the society due to different policies. Thus, we can prepare an index number of wages, imports, exports, industrial production, unemployment, profit, area under cultivation, enrolment in a college, etc.

Used for Comparing data:

We can compare, with the help of index numbers, economic conditions of a class of people at two different periods.

Gives the knowledge of the exact change in standard of living: 

It helps to measure standard of living by comparing cost of living and price level. So, the exact living standard of people can be known. Income may increase but if the index number shows a decrease in the value in money, then there is decrease in the living standard.

Helps in the measurement of the inflation rate:

Index number helps to know the inflation rate by measuring price level and value of money between two periods. It helps Central Bank in deciding credit policy.

Helps in adjustment in salaries and allowances: 

Index number helps to determine wages and allowance of employees. Adjustment in the wages and salaries are made according to the cost of living. Cost of living index number is a useful guide to the government and private enterprises to make necessary adjustment in salaries and allowances of the workers. The extent of dearness allowance is decided by the cost of living index.

It is useful to business community: 

Index number is very useful in planning and decision making process of the business firm. 

It provides information regarding foreign trade: 

It is used to compare imports and exports of two different periods. So, it provides key information about the volume of foreign trade. Index of exports and imports provides useful information regarding foreign trade. Using which Government can decide EXIM policy.

Limitation of Index Number:

Not completely true: 

Index number not fully true because they are simply rough indications (approximations) of the relative changes. They cannot be taken as infallible guides. Their data are open to question and they lead to different interpretations. The index number simply indicate arithmetical tendency of the temporal changes in the variable. The choice of representative commodities may lead to fallacious conclusions as they are based on samples. If there are errors in the choice of base periods or weights, etc. then result is not reliable.

International comparison is not possible: 

International comparisons are difficult, if not impossible, on account of the different bases, different sets of commodities or difference in their quality or quantity. Hence index numbers do not help international comparisons.

Difference of time: 

Comparison between different times are is not easy. Over long periods, some popular commodities are replaced by others or consumption habits of people got changed. Entirely new types of commodities come to figure in. With the passage of time, it is difficult to make comparison of index number. Thus comparisons of changes in variables over long periods are not reliable.

Limited use: 

Index numbers are prepared with certain specific objective. If they are used for another purpose they may lead to wrong conclusion. Index numbers measure only changes in the sectional price levels. For another section an entirely different set of commodities will have to be selected. Different people use different things and hold different assets. Therefore, different classes of people are affected differently by a given change in the price level. Hence, the same index number cannot throw light on the effects of price changes on all sections of society. Thus they may be useful for one purpose but not for another.

Lack of retail price index number: 

Most of the index numbers are prepared on the basis of wholesale prices. But in real life, retail prices are most relevant, but it is difficult to collect retail prices.

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Management > Managerial Statistics > Introduction to Index Numbers