Index NumbersClass 11 Statistics For Economics Notes

Introduction to Index Numbers

Have you ever wondered how we can say "prices are rising" when some things get more expensive, some get cheaper, and others stay the same? It's confusing to track every single price change. Economists and policymakers face the same problem on a much larger scale, whether they're looking at industrial output, stock markets, or the cost of living.

Index numbers are the solution. They are a statistical tool that summarizes the changes in a group of related variables into a single, easy-to-understand figure.

• An industrial worker earned ₹1,000 in 1982 and now earns ₹12,000. Has their standard of living really increased 12 times? An index number can help us understand the real change by accounting for inflation.
• Newspapers report that the Sensex (a stock market index) is rising or falling. What does this single number tell us about the health of the economy and investors' wealth?
• How does the government measure inflation, the general rise in prices, to make policy decisions?

What is an Index Number?

An index number is a statistical device used to measure the average change in a group of related variables over time or between two different situations. It simplifies complex data into a single representative figure.

Key characteristics of an index number:

• Measures Change: It measures changes in variables like prices of goods, volume of industrial production, or cost of living.
• Expressed as a Percentage: Conventionally, index numbers are shown as percentages to make comparison easy.
• Uses a Base Period: To measure change, we need a starting point. This is called the base period. The index number for the base period is always set to 100.
• Shows Proportional Change: Any other period's index number is compared to the base of 100.

Types of Index Numbers

• Price Index Numbers: These are the most common type and measure changes in the prices of goods.
• Quantity Index Numbers: These measure changes in the physical volume of production, construction, or employment.

Construction of an Index Number

There are two main methods for constructing an index number: the Aggregative Method and the Method of Averaging Relatives. We will explore these using price index numbers as an example.

The Aggregative Method

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

Simple Aggregative Method

This is the simplest method, where we just add up the prices of all commodities.

• P₀₁ is the price index of the current period (1) with respect to the base period (0).
• ΣP₁ is the sum of the prices of all commodities in the current period.
• ΣP₀ is the sum of the prices of all commodities in the base period.

This method has a major limitation: it is unweighted. It treats all items as equally important. In reality, a change in the price of a staple food item like wheat has a much bigger impact on a family's budget than a change in the price of a luxury item.

Weighted Aggregative Method

To overcome the limitation of the simple method, we use a weighted index, which accounts for the relative importance of different items. In price indices, the "weights" are typically the quantities of goods consumed.

There are two main types of weighted aggregative price indices:

1. Laspeyre's Price Index This method uses the quantities consumed in the base period (q₀) as weights. It answers the question: "If we bought the same basket of goods as we did in the base year, how much more would it cost us today?"

2. Paasche's Price Index This method uses the quantities consumed in the current period (q₁) as weights. It answers the question: "How much would our current basket of goods have cost us back in the base year?"

Method of Averaging Relatives

This method first calculates the price relative for each commodity and then finds the average of these relatives. A price relative is simply the price of a single commodity in the current period as a percentage of its price in the base period.

Price Relative = (P₁ / P₀) × 100

Simple Average of Price Relatives

This method calculates the simple arithmetic mean of the price relatives of all commodities.

Weighted Average of Price Relatives

This is a more refined method where each price relative is assigned a weight (W) based on its importance, often determined by the proportion of expenditure on that item.

The weights are typically based on expenditure in the base period because it's inconvenient to calculate new weights every year.

Some Important Index Numbers

Several index numbers are widely used in India and around the world to track economic activity.

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 (like industrial workers or agricultural labourers).

In India, government agencies prepare several CPIs, including:

• CPI for Industrial Workers (CPI-IW)
• CPI for Agricultural Labourers (CPI-AL)
• CPI for Rural Labourers (CPI-RL)
• All-India Combined CPI (Rural + Urban), which the Reserve Bank of India uses as the main measure of inflation.

Wholesale Price Index (WPI)

The Wholesale Price Index (WPI) measures the change in the general price level of goods at the wholesale level, before they reach the consumer.

• It does not include services (like barber charges or repairs).
• It does not refer to a specific consumer group.
• The inflation rate calculated from WPI is often called "Headline Inflation".
• Economists also look at "Core Inflation", which excludes volatile food and fuel prices from the WPI to see the underlying trend.

Index of Industrial Production (IIP)

Unlike the CPI and WPI, the Index of Industrial Production (IIP) is a quantity index. It measures the changes in the volume of production in the industrial sector.

• It is a weighted arithmetic mean of quantity relatives.
• The main sectors covered are Mining, Manufacturing, and Electricity.
• A special focus is often given to the Eight Core Industries (e.g., coal, crude oil, steel, electricity), which have a significant weight in the IIP.

Sensex

The Sensex is the benchmark index of the Bombay Stock Exchange (BSE), with 1978-79 as its base period.

• It consists of 30 major stocks from various sectors of the economy.
• A rising Sensex generally indicates that investors are optimistic about the future performance of companies and the overall economy.

Issues in the Construction of an Index Number

Constructing a reliable index number involves several important considerations:

• Purpose of the Index: The purpose must be clear. A price index cannot be used to measure changes in production volume.
• Selection of Items: The items included must be representative of the group being studied. For example, a rise in petrol prices has a different impact on an agricultural labourer than on an urban professional.
• Choice of Base Year: The base year should be a "normal" year, free from extreme events like wars or famines. It should also not be too far in the past, as consumption patterns change over time.
• Choice of Formula: The choice between Laspeyre's, Paasche's, or other formulas depends on the specific question being analyzed.
• Data Collection: The data used must be reliable. Using poor-quality data will lead to misleading results.

Index Numbers in Economics

Index numbers are indispensable tools for economic policy-making and analysis.

• Wage and Policy Formulation: CPI is used for wage negotiations, income policy, and taxation. If the cost of living rises, wages may need to be adjusted upwards.
• Measuring Inflation: WPI is widely used to measure the rate of inflation, which is a sustained increase in the general price level.
• Deflating Economic Data: WPI helps to remove the effect of price changes from economic data like national income, allowing for a comparison of "real" growth over time.
• Calculating Real Wage and Purchasing Power: CPI helps determine the actual value of money.
  • Purchasing Power of Money = 1 / Cost of Living Index
  • Real Wage = (Money Wage / Cost of Living Index) × 100

• Tracking Economic Performance: IIP provides a clear figure on the change in industrial production, while the Sensex acts as a barometer for investor confidence and stock market performance.