Introduction to Index Numbers

Introduction

Index numbers are used for measuring changes in a specific variable or group of variables regarding location, time, or other constraints. The index number in statistics is one of the most used statistical methods for measuring changes considering specific characteristics of a variable. For example, index numbers can evaluate changes in the price of particular commodities or different geographical locations to understand inflationary and deflationary tendencies related to the product. In addition to this, index numbers reflect the barometers of the economic activities by serving as a tool for indicating agricultural production, industrial production, business activities, and other statistical information. Thus, index number can be defined as the relative measure used for comparing and describing numerical changes in the prices, quantity, and other aspects of a commodity regarding varied elements.

Key uses of Index Numbers

Index numbers are used for the following aspects:

• Index numbers work as economic parameters that reflect changes in the economy in the form of inflationary and deflationary tendencies.  
• Index numbers are used for measuring relative changes over a successive period of time for statistically measuring and depicting trends so general tendencies related to any product or service can be determined, evaluated, and forecasted.
• Index numbers are generally represented in percentages, so they are highly useful in comparing varied commodities and understanding changes with specific constraints.
• Index numbers frame business and economic policies as they depict the necessity of change in alignment with the changes noted in evaluated constraints.
• Price index numbers are used deflating as they connect the original data for comparison with notable changes and support the determination of purchasing power in the monetary unit.
• Index numbers help compare the standard of living in different periods and times so that governing bodies can take necessary welfare measures.
• Index numbers provide a basic idea about the averages of homogenous units, which can be measured from varied perspectives.

Types of Index Numbers

Price Index Numbers

The price index is considered a particular sort of average of homogenous units. It represents the net relative changes in commodities prices and can be expressed in different units. As evident from the name of this sort of index number, it depicts changes and percentages about prices. Price index numbers are further bifurcated in wholesale price index numbers and retail price index numbers that represent changes in wholesale prices and retail prices of commodities, respectively.

Quantity Index Numbers

This type of index number is concerned with measuring changes in the number of commodities, such as the number of commodities consumed, purchased, and produced. Thus, this type of index number helps make comparisons and analyze quantity or volume.

Value Index

Value index numbers are concerned with evaluating the changes incurred in the total value of products over a certain period by considering the total value of the base period as the foundational constraints.

Methods of Constructing Index Numbers

Methods of constructing index numbers can be divided into two parts :-

Unweighted 

• Simple Aggregative
• Simple Average of Price Relatives

Weighted 

• Weighted  Aggregative
• Weighted Average of Price Relatives

Unweighted Index Numbers

An unweighted price index number tends to measure the change in the process of a single commodity or group of commodities in percentage form between two different periods. In unweighted index numbers, all the values evaluated in the study tend to hold equal significance. Sub-methods of unweighted index numbers are as follows:

• Simple Aggregative Method

This method evaluates prices of different items in current years by adding all the prices, dividing the sum by the prices during base years, and multiplying by 100. It is a relatively easy method to employ. However, the relative importance of the commodities is not taken into consideration. In addition to this, high-priced commodities tend to influence derived index numbers.

• Simple Average of Price Relatives

There are varied steps employed in this method. First of all, prices of all relatives are gathered for varied commodities, and the average of gathered prices is calculated using geometric mean or arithmetic mean formulas. Price relative can be understood as the price of the current year, which is expressed as the percentage form regarding the price of the base year. The key advantage of this method is that the extreme prices of the items do not influence it, yet all the items have equal importance in calculating the index number. In addition to this, price relatives are derived as purely numeric values. The value of the average price relative index is not influenced by the units or volume of commodities included in the process of deriving index numbers. 

On the other hand, one of the key limitations of this method is that equal weight is assigned to every commodity, which gives equal importance to every price relative. In actual practice, every price relative does not hold equal importance.

Weighted Index Numbers

For computing weighted index numbers, weights are assigned to each item in such a way that it reflects their economic importance. In most cases, the volume or value of consumed quantities is used as weights. There are two sub-methods for calculating weighted index numbers.

• Weighted Aggregative

This method focuses on evaluating the price of each commodity by weighting them based on quantity sold either in the base year or the current year. There are various formulae for assigning weights; thus, many methods exist for constructing index numbers. Lasperyre’s Index, Paasche’s Index, Dorish and Bowley’s Index, Fisher’s Ideal Index, Marshall-Edgeworth Index, and Kelly’s Index are the key methods for assigning and calculating weighted aggregates.

• Weighted Average of Price Relatives

A weighted average of price relatives is computed by assigning weights to the unweighted price relatives. Additionally, arithmetic or geometric mean is used for averaging the weighted price relatives.

Consumer Price Index Numbers

Consumer price index numbers are generally computed for evaluating the effect of change in prices of the commodities on its consumers. The indices provide an overview of the average increase in the expenses so that living from the base year can be maintained by making necessary changes. On the other hand, general index numbers often lack the impact of change in general price levels on the cost of living for individuals from different classes at different times. The key reasons for which consumer price index numbers are calculated are as follows:

• It helps negotiate wages, contracts, financial adjustments, and dearness allowances.
• For governing bodies, set up and alter wage policies, price policies, rent control, economic policies, and taxation policies.
• It helps measure changes in purchasing power of money and fluctuations in real income.
• It helps in analyzing the market prices for specific types of goods and services.
• Consumer price index numbers also reflect the cost of living index numbers.

Considerations for Constructing Index Number

Following are a few considerations to be undertaken before constructing index numbers from statistical data:

• Determine the purpose of index numbers
• Adequate selection of base period
• Determine the commodities to be evaluated
• Selecting price quotations to be evaluated
• Selecting adequate volume and weight for evaluation
• Determination of proper unit of average
• Using adequate and appropriate formula