Index Number

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 Index Number

The index number helps in studying changes in consumption, production, imports, exports, cost of living, crimes, accidents, national income, business failures, and other phenomena.


Background of Index Numbers

The index number was first constructed by an Indian Statistician, Carli in 1764. It was used for the first time to compare the prices of the year 1750 with that of the year 1500. An index number is a statistical tool for measuring changes in the magnitude of a group of related variables.

 Index Numbers are devices for measuring differences in the magnitude of a group of related variables."- Croxton and Cowden

Characteristics of Index Numbers

1. Specialized Averages

2. Expressed in Percentages

3. It assesses the impact of changes with respect to time or location

4. It measures the change that can not be measured directly

Uses of Index Numbers

1. Measurement and Comparison of Changes in the Price Level

2. Helps in Policy Formulation -  An index number is an important tool for government or non-government organizations in the following ways:

In policy formulation, there is a need for a base or trend. With the index numbers, the trends of different phenomena can be studied.

It can also be utilized in the formulation and planning of government and business policies.

3. Acts as an Economic Barometer:

A barometer is an instrument that is used to measure atmospheric pressure. It indicates fluctuations in the general conditions of a country and measures the pulse of the economy.

4. Helps in Studying Trade:

Index numbers are useful in studying the trend of a series over a period of time. It helps in forecasting future trends which is crucial for any business or production activity's future operations. Besides, it also aids in determining patterns in exports, imports, prices, and several other occurrences.

Limitations of Index numbers

The limitations of Index Numbers are as follows:


1. Provides Relative Changes only:

Index Numbers estimate relative changes only and cannot speak the truth as they are only approximate indicators.

2. Lack of Perfect Accuracy:

Index numbers do not consider every item and are based on the sample items. Thus, in case of an inadequate sample or a sample selected through a faulty process, there will be inaccurate results.

3. Ignores Qualitative Changes:

Index numbers do not pay any attention to the qualitative changes in the product while constructing the price or production. An increase in the price possibly results from the improvement in the quality of the product. But it is neglected in the index numbers.


4. Possibility of Manipulations:

Index numbers can be created in a way that allows for manipulation. This manipulation can be made in a selection of a particular base year, a particular group of commodities, a specific set of prices, etc.


5. Difference between purpose and method of Construction:

When the index numbers are created for a specific purpose using a specific methodology, they are not suitable for all situations and uses.

Construct of Index Number 

The Aggregative Method

An index number can be computed by the aggregative

method and by the method of averaging relatives.

1. Simple Aggregative Method

The formula for a simple aggregative price index is:

P01=P1/P0 X100

where,

P1= Price of the commodity in the current period and

P0= Price of the commodity in the base period


 


2. Weighted Aggregative Method

Laspeyre’s Price Index: The formula for a weighted aggregative price index under Laspeyre’s method is:

2. Paasche’s Price Index: The formula for a weighted
aggregative price index under Paasche’s method is:
3. Fisher's Ideal Index  Number

Method of Averaging relatives
1. Simple price relative index
When there is only one commodity, the price index is the ratio of the price of the commodity in the current period to that in the base period, usually expressed in percentage terms.
The method of averaging relatives takes the average of these relatives when there are many commodities. The price index number using price relatives is defined as:








Types of Index Number
1. Consumer Price Index (CPI)
Consumer price index (CPI), also known as the cost of living index, measures the average change in retail prices.
Consider the following statement: CPI for industrial workers (2001 = 100) is 278 in May 2020. What does this statement mean? It means that if the industrial worker was spending `100 in 2001 for a typical basket of commodities, he needs `278 in May 2020 to be able to buy an identical basket of commodities. It is not necessary that he/she buys the basket. What is important is whether he has the capability (purchasing power) to buy it.

CPI can be measured by the following two methods.
They may give different answers.
1. Family Budget Method: Consumer price index
(CPI) or the cost of living index is calculated as follows:

2. Aggregate Expenditure Method: CPI or the cost of living index is calculated as follows:

2. Wholesale Price Index (WPI)
The Wholesale price index number indicates the
change in the general price level. Unlike the CPI, it does not have any reference consumer category. It does not include items pertaining to services like barber charges, repairing, etc.
What does the statement “WPI with 2011–12 as base is 112.8 in May, 2017” mean? The Wholesale Price Index is now being prepared with base 2011–12 = 100. The value of the index for May 2017 was 112.8. It means that the general price level has risen by 12.8 per cent during this period. 
WPI uses the prices that are prevailing at the wholesale level. Only the prices of goods are included. The main types of goods and their weights are as follows:

Usually the data on Wholesale Prices is available quickly. The ‘All Commodities Inflation Rate’ is often referred to as ‘Headline Inflation’. Sometimes, the focus is on food items which comprise 24.23% of the total weight.

Inflation and Index Numbers

The WPI is widely used to measure the rate of inflation.
Inflation: Inflation is a general and continuing increase in prices.

If inflation becomes sufficiently large, its primary impact lies in lowering the value of money.

where, Xt and Xt–1 refer to the WPI for the tth and (t – 1)th weeks. 
CPI is also used in calculating the purchasing power of money and real wage.



Importance of Index Numbers
1. To simplify complicated matters: Index numbers present the given information in such a manner that it can be easily understood.
2. To measure comparative changes: Index
numbers facilitate comparison of change from
time to time, among different places and in series expressed in different units. The changes in price level, cost of living, etc. which are not capable of measurement directly are measured with the help of index numbers.
3. To frame suitable policies: Index numbers guide a lot in framing suitable economic policies.
For example, wholesale and retail price index numbers help in economic and business policy-making regarding price, output, demand, sales, etc. The indices of consumption of various commodities help in the planning of their future production. Index numbers are applied with advantage for formulating and revising their policies from time to time.
4. To measure the purchasing power of money: Index numbers are helpful in measuring the purchasing power, i.e., value of the money. This helps in fixing proper wage policy in the country.
5. To study trends and to make forecast: Index numbers are most widely used for measuring changes over a period of time. On the basis of present indices, the forecast for the future can be made.

Steps involved in the calculation of
Consumer Price Index (CPI)
1. Selection of the Consumer Class: First of all, it
should be determined, for whom CPI is to
calculate i.e., for industrial labour, farmers, govt employees etc. 
Information about the Family Budget: After the
selection of consumer class, information about
their family budget should be collected i.e., what
they consume, how much they consume, prices of the concerned goods and services etc.
3. Choice of Base Year: After this, base year
selection should be done. It should be a normal
year without much ups and downs.
4. Information about Prices: The data regarding
retail prices of selected goods and services should be collected from the concerned area, where the selected consumer group lives and makes the purchases. 
5. Weightage: Selected items should be given
weights according to their relative importance.
6. Selection of Method: At the end, it should be
decided that aggregative expenditure method
should be used or family budget method should be used to measure CPI.

Importance of Consumer Price Index (CPI)
or Cost of Living Index
1. Formulation of policies: CPI helps the
government in formulation of various policies
regarding taxation, prices, rent control, fiscal
policy, general economic policies, etc.
2. Determination of dearness allowance (DA):
CPI helps in the determination of dearness
allowance, on the basis of government employees' salaries are hiked to compensate the rising price level.
3. To calculate the purchasing power of money
and real wage: CPI or Cost of Living Index is also
used in calculating the purchasing power of money and real wage.


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