You have already learned how to obtain summary measures from a large amount of data. Now, we will explore how to find summary measures of change in a group of related variables.
Imagine these scenarios:
Rabi’s Market Experience:
Rabi visits the market after a long time and notices that the prices of various items have changed. Some have become costlier, while others are cheaper. When he tries to explain the changes to his father, listing every single price change becomes confusing and hard to understand.
Changes in the Industrial Sector:
The industrial sector is made up of many subsectors. Some of them are growing, while others are declining. The rates of change are not uniform, making it difficult to explain the overall trend. A single figure that summarizes all these changes would be helpful.
Examples Illustrating Index Numbers
Case 1:
An industrial worker earned Rs 1,000 in 1982. Today, his salary is Rs 12,000.
Case 2:
You often read about the Sensex in newspapers.
Case 3:
The government claims that an increase in petroleum prices will not cause inflation to rise too much.
The Need for Index Numbers
These examples show the need for a single figure that can summarize complex changes happening over time or across different sectors. Index numbers help us do that by providing a way to compare changes and understand trends in a simple manner.
An index number is a statistical tool used to measure changes in the magnitude of a group of related variables. It helps in understanding the general trend of changes over time or across different situations.
Types of Index Numbers
1. Price Index Numbers:
2. Quantity Index Numbers:
Constructing an index number involves using statistical methods to compare changes over time. Here, we'll focus on price index numbers as examples.
There are two methods of constructing index numbers:
In this method, the prices of different commodities are added together for both the base period and the current period.
Where,
Example: Calculation of Simple Aggregative Price Index
The index number is 138.5, indicating a 38.5% rise in prices.
Unlike the simple method, this method gives different weights to different commodities based on their importance.
Formula:
Where,
There are two types of weighted aggregating price indices: Laspeyre’s Price Index and Paasche’s Price Index. Let's understand them with the help of an example.
Example: Calculation of Weighted Aggregative Price Index (Laspeyre’s Price Index)
The index number is 135.3, meaning prices have increased by 35.3%.
Laspeyre’s Price Index
Paasche’s Price Index (Using Current Period Quantities)
Instead of using the base period quantities, it uses the current period quantities as weights.
The Paasche’s index tells us:
Comparison:
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, expressed in percentage terms.
However, when there are many commodities, the method of averaging relatives is used.
Formula (Simple Average of Price Relatives):
Where:
Example
Imagine we are comparing the prices of 4 different commodities over two periods: the base period (earlier) and the current period (later). We want to find out how much the prices have increased on average.
Given Data:
Step 1: Calculate the Price Relative for Each Commodity
The price relative for a commodity is calculated using the formula:
Where:
Step 2: Calculate the Average of the Price Relatives
Now, we add all the price relatives and divide by the number of commodities (which is 4 here):
Step 3: Interpret the Result
The final value of 149 means that, on average, the prices of these commodities have increased by 49% compared to the base period.
Instead of simply averaging, this method uses weights to reflect the relative importance of items. The weights may represent the proportion of expenditure on each item out of the total expenditure.
Formula (Weighted Average of Price Relatives)
Where:
Example:
The weighted price index is 156, which means prices have risen by 56%.
Why are Weighted Index Numbers Useful?
The higher rise in the weighted index compared to the simple index shows the importance of considering the relative weights of commodities. For instance, a large increase in the price of a major commodity (like food) will impact the overall price index more significantly than an increase in the price of a less important commodity (like cloth).
The Consumer Price Index (CPI), also known as the cost of living index, measures the average change in retail prices of goods and services over time.
It shows how much the prices have increased or decreased compared to a base year.
If the CPI for industrial workers with a base year of 2001 = 100 is 277 in December 2014, it means:
If an industrial worker spent Rs. 100 in 2001 to buy a typical basket of commodities, they would need Rs. 277 in December 2014 to buy the same basket.
This indicates an increase of 177% in prices compared to the base year.
The formula for CPI is:
Example
Calculation:
The CPI value is 97.86, which is less than 100. This means the cost of living has decreased by 2.14%.
If the CPI is greater than 100, it indicates an increase in the cost of living, and wages/salaries need to be adjusted upwards by the amount exceeding 100.
If the CPI is less than 100, it indicates a decrease in the cost of living.
The Wholesale Price Index (WPI) measures the changes in the general price level of goods at the wholesale level (not retail level).
It does not include services like barber charges, repairs, etc.
If the WPI with the base year 2004-05 = 100 is 253 in October 2014, it means:
The general price level has risen by 153% during this period compared to the base year.
Base Year: 2011-12 = 100.
WPI Value for May 2017: 112.8.
It only includes the prices of goods (not services).
Important concepts:
Headline Inflation (All Commodities Inflation Rate):
It measures overall inflation by considering price changes of all goods included in the Wholesale Price Index (WPI). It provides a broad view of price changes across various sectors like Primary Articles, Fuel & Power, and Manufactured Products.
WPI Food Index:
This index focuses on price changes of food items, including:
Core Inflation:
Excludes volatile items like food and fuel to focus only on manufactured goods. This helps analyze long-term inflation trends and makes up around 55% of the total WPI weight.
The Human Development Index (HDI) is a comprehensive measure that seeks to capture three crucial aspects of human development, namely access to education and knowledge, a reasonable standard of living, and good health and longevity. Essentially, the HDI is used to gauge the extent to which development has positively impacted the quality of life for humans.
Index numbers are crucial in economic policy-making. They provide valuable insights into economic trends and assist policymakers in making informed decisions.
Index numbers can be used for:
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1. What is the purpose of constructing index numbers? | ![]() |
2. What are the methods used for constructing index numbers? | ![]() |
3. How are simple index numbers constructed? | ![]() |
4. What is the difference between simple and weighted index numbers? | ![]() |
5. What are some important index numbers used in economics? | ![]() |