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Index Numbers and Time Series

Introduction, Characteristics, Uses, Types, Method of Constructing Unweighted Index numbers

INDEX NUMBERS
Definition : Index Numbers are used to measure the change in some quantity which we cannot observe directly.

From the given definition, the following features of index numbers can be derived.
• Index numbers are used to depict relative changes in variables; that is, they analyse changes in a variable with respect to a base year (a standard point of comparison).
• These numbers are generally expressed in the percentage form. The idea behind using the relatives is that it is easier to compare the relatives and these relatives can be easily added.
• With the help of an index number, two series with different units can also be compared easily. Thus, an index number is said to be a specialised average.
• An index number helps in estimating the absolute quantitative changes in variables. For example, if the price index is 130 in 2008 compared to 100 in 2002, then this suggests that the price has risen by 30%. However, it must be noted that even if the index shows a rise in the price level by 30%, there may be some commodities whose prices must have fallen.

Characteristics of Index Numbers

1) Index Numbers can be expressed in numbers only, though the change can be expressed in words also, but the index numbers represents these change numbers.

2) Index numbers are of special type of average because in simple average data are uniform and their units are also even, whereas in index numbers the data having different measurement units are also used for these percentages as price relatives. Price relatives are averaged for computing index numbers.

3) The index numbers are comparative in nature because they measure relative changes and relative changes are computed on the basis of some other data so it  can be  said that index  numbers are comparative in nature.

4)  Index numbers are used to measure the changes in prices in the group of items but the changes in the quantity of agricultural production, imports, and exports can also be measured through index numbers. Hence, they act as a Universal Utility.

Basic Types of Index Numbers

i.  Price Index
ii. Quantity Index
iii. Value Index
iv. Specific Index

i. Price Index: Price index is an index that measures overall changes in the price levels of a commodity in the economy between two periods. These prices can either be retail or wholesale.

Simple price index =

The following note describes the two types of index numbers.

ii. Quantity Index: It measures overall changes in the physical quantity of  goods produced, consumed or sold in the economy between two periods. This index helps in taking production decisions. It is periodically used for the commodities that are subject to price variations.

Quantity index =

iii. Value Index: It facilitates comparison of the total value produced (Price $×$ Quantity) in the current year with that produced in the base year.

Value index

iv. Specific Index: It includes all those indices that are computed by various researchers, industrial units, etc. in order to get some specific or purposive information. For instance, the index of industrial production, index used for tracking the commercial efficiency, index for job opportunities in different geographical areas over two period of time are some of the specific indices. These are also known as special purpose index numbers.
The following is a brief explanation of the Index of Industrial Production.

Difficulties in the Construction of Index Numbers

The construction of index numbers involves various difficulties. Some of the issues related to the construction of a purposeful index number are as follows.

1. Objective: Different index numbers serve different objectives. Thus, based on the purpose of a study, an appropriate index number is chosen. For example, if we have to study the changes in the cost of living, we will construct a consumer price Index.

2. Base period selection: Base year refers to the year against which the values of a variable (such as price, wages, quantity) in the current year are compared. While constructing an index number, it is necessary to choose an appropriate base year, as it serves as the reference year for analysing changes in the variable.

A base year should have the following features.
i. The base year should be neither less than a month nor longer than a year.
ii. It should be neither too close nor too far from the current year. Too far a base year would not track the various changes (such as changes in the taste and preferences, habits and customs) that might take place in the course of time. Similarly, too near a base year would measure only slight changes in the variable in the two periods.
iii. It should also be normal and free from any kind of abnormalities or fluctuations such as natural calamities and business cycles.

Note: The index number for a base year is always equal to 100.

3. Item selection: Index numbers are generally constructed with respect to a variable. However, it is important to decide the appropriate unit of the variable involved. For example, while constructing the price index, whether retail price or wholesale price should be used or not depends on the objective or the purpose. Emphasis should also be laid on deciding the time period to be considered for these prices. In practice, an average of price for a specific period is usually preferred.

4. Reliable source of data: For the construction of suitable index numbers, the source from which data is collected also plays an important role. The data must be collected from a reliable source so that it is accurate and helps to derive significant conclusions.

5. Choice of an average: An index number involves the use of any average such as mean, median or mode. However, median and mode are found unsuitable for deriving meaningful conclusions. Theoretically, geometric mean is considered a better measure of averaging relatives, whereas, in practice, arithmetic mean is widely used due to its simplicity.

6. Suitable weighting system: It is necessary to assign suitable weights to different items in an index as per their relative importance in the index. For example, while constructing the consumer price index, more weight is given to food crops like wheat, rice, etc. rather than tea, coffee, etc.

7. Suitable method: There are numerous methods for calculating index numbers such as the aggregative method and the price relative method. Similarly, for the calculation …

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