Introduction to Index Numbers

In our daily lives, we often encounter situations where many related variables are changing simultaneously. For example, the prices of some commodities in the market may rise while others fall. The output of various industrial subsectors may increase or decrease at different rates. Describing each of these individual changes can be confusing and overwhelming.

An index number is a statistical device that provides a solution to this problem. It is a specialised average designed to measure the changes in the magnitude of a group of related variables over time or between different locations. It summarises these diverging changes into a single, representative figure.

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What is an Index Number?

An index number is a statistical measure of the average change in a group of related variables over two different situations. It helps answer questions like:

• An industrial worker earning ₹1,000 in 1982 now earns ₹12,000. Has his standard of living actually increased 12 times?
• What does it mean when the Sensex crosses 8000 points?
• How does the government measure the rate of inflation?

Conventionally, index numbers are expressed as a percentage. The period with which a comparison is made is called the base period, and its value is always taken as 100. The period being compared is the current period. If the index number for the current period is 250, it means the value has increased to two and a half times that of the base period.

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Types of Index Numbers

• Price Index Numbers: These measure and permit comparison of the prices of a specific list of commodities over time.
• Quantity Index Numbers: These measure the changes in the physical volume of production, construction, or employment.

Construction of an Index Number

Constructing a price index number involves summarising the price changes of many different commodities into a single number. There are two primary methods for this: the aggregative method and the method of averaging relatives.

1. The Aggregative Method

This method involves aggregating the prices of commodities in the base and current periods and then comparing them.

a) Simple Aggregative Price Index

This is the simplest method, where the sum of prices of all commodities in the current period is divided by the sum of their prices in the base period.

Formula: $ P_{01} = \frac{\sum P_1}{\sum P_0} \times 100 $

where $\sum P_1$ is the sum of current period prices and $\sum P_0$ is the sum of base period prices.

This index has a major limitation: it is unweighted, meaning it treats all commodities as equally important, which is rarely true in reality. For example, a 10% rise in the price of wheat has a much greater impact on a household budget than a 10% rise in the price of salt.

b) Weighted Aggregative Price Index

To overcome the limitation of the simple index, a weighted index is used. In this method, the relative importance (or weight) of each item is taken into account. For price indices, the quantity consumed is typically used as the weight.

• Laspeyre’s Price Index: This method uses the base period quantities ($q_0$) as weights. It measures the changing value of a fixed basket of goods from the base period.

  Formula: $ P_{01} = \frac{\sum P_1 q_0}{\sum P_0 q_0} \times 100 $

• Paasche’s Price Index: This method uses the current period quantities ($q_1$) as weights. It measures the change in price for the basket of goods consumed in the current period.

  Formula: $ P_{01} = \frac{\sum P_1 q_1}{\sum P_0 q_1} \times 100 $

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2. Method of Averaging Relatives

This method involves calculating a price relative for each commodity and then taking an average of these relatives.

Price Relative for a commodity = $ \frac{P_1}{P_0} \times 100 $

a) Simple Average of Price Relatives

This is the simple arithmetic mean of the price relatives of all commodities.

Formula: $ P_{01} = \frac{\sum \left( \frac{P_1}{P_0} \times 100 \right)}{n} $, where 'n' is the number of commodities.

b) Weighted Average of Price Relatives

This is the weighted arithmetic mean of price relatives, where the weights (W) are usually the value shares of commodities in the total expenditure.

Formula: $ P_{01} = \frac{\sum W \left( \frac{P_1}{P_0} \times 100 \right)}{\sum W} $

Using base period expenditure ($P_0 q_0$) as weights gives a result identical to Laspeyre's index.

Some Important Index Numbers in India

Several key index numbers are regularly compiled and used in India to track the economy.

1. Consumer Price Index (CPI)

The Consumer Price Index (CPI), also known as the cost of living index, measures the average change in the retail prices of a basket of goods and services consumed by a specific group of people (e.g., industrial workers, agricultural labourers).

Interpretation: If the CPI for industrial workers (base year 2012=100) is 131.4 in May 2017, it means that a basket of goods that cost ₹100 in 2012 would cost ₹131.40 in May 2017. It is used to adjust wages and salaries to maintain the purchasing power of consumers.

The Reserve Bank of India now uses the All-India Combined Consumer Price Index as the main measure of how consumer prices are changing.

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2. Wholesale Price Index (WPI)

The Wholesale Price Index (WPI) indicates the change in the general price level by tracking the prices of goods at the wholesale level. It does not include services. The WPI is often used to measure the headline inflation rate in the economy.

Interpretation: If the WPI (base year 2011-12=100) is 112.8 in May 2017, it means the general price level of wholesale goods has risen by 12.8% since the base year.

The main components and their weights in the WPI (2011-12 series) are:

• Primary Articles: 22.62%
• Fuel and Power: 13.15%
• Manufactured Products: 64.23%

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3. Index of Industrial Production (IIP)

The Index of Industrial Production (IIP) is a quantity index that measures the changes in the volume of production in the industrial sector. It is a weighted arithmetic mean of quantity relatives. The current base year is 2011-12=100.

The main industrial sectors and their weights are:

• Mining: 14.4%
• Manufacturing: 77.6%
• Electricity: 8.0%

The IIP provides a quantitative figure about the change in industrial output and is a key indicator of economic performance.

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4. Sensex

The Sensex is the benchmark index of the Bombay Stock Exchange (BSE), with a base year of 1978–79. It consists of 30 large, well-established, and financially sound companies listed on the BSE. A rising Sensex indicates investor optimism about the health of the economy and the future earnings of companies.

Issues in the Construction of an Index Number

Constructing a meaningful and accurate index number involves several important considerations:

1. Purpose of the Index: The purpose must be clearly defined. The choice of items, formula, and base year all depend on what the index is intended to measure. A price index cannot be used to measure changes in volume.
2. Selection of Items: The items included in the index must be representative of the group they are meant to describe. For a CPI, items must be relevant to the consumption patterns of the target consumer group.
3. Choice of the Base Year: The base year should be a "normal" year, free from extreme events like droughts, wars, or economic crises. It should also not be too far in the past, as consumption patterns and products change over time. Base years are routinely updated to maintain relevance.
4. Choice of Formula: The choice between different formulas (like Laspeyre’s and Paasche’s) depends on the specific question the index is supposed to answer. Each has its own interpretation and bias.
5. Source of Data: The reliability of an index number depends on the quality of the data used. Care must be taken to collect accurate data or use reliable secondary sources.

Uses of Index Numbers in Economics

Index numbers are vital tools in economics and policy-making. They have a wide range of applications:

• Wage and Salary Adjustments: CPI numbers are used in wage negotiations and for adjusting salaries (e.g., Dearness Allowance for government employees) to compensate for the rising cost of living.
• Formulation of Policies: Index numbers are crucial for formulating income policy, price policy, rent control, and general economic policies.
• Measuring Inflation: The WPI is widely used to measure the rate of inflation, which is a general and continuing increase in prices.
• Deflating Economic Aggregates: Price indices like the WPI are used to eliminate the effect of price changes from economic aggregates like national income to measure "real" growth.
• Calculating Purchasing Power and Real Wages: CPI is used to calculate the purchasing power of money and to convert money wages into real wages.
  • Purchasing Power of Money = $ \frac{1}{\text{Cost of Living Index}} $
  • Real Wage = $ \left( \frac{\text{Money Wage}}{\text{Cost of Living Index}} \right) \times 100 $
• Monitoring Economic Performance: The Index of Industrial Production (IIP) and the Agricultural Production Index provide ready reckoners of the performance of these key sectors.
• Guiding Investors: The Sensex serves as a useful guide for investors in the stock market, reflecting market sentiment and economic health.

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