Unit Structure
9.0 Overview
9.1 Learning Objectives 9.2 Index Numbers
9.3 Methods of Construction of Index Numbers 9.3.1 Index Numbers of Prices
9.3.2 Two Approaches 9.3.3 Worked Examples 9.3.4 Fisher’s Index of Prices
9.3.5 General Formulae for Index Numbers 9.3.6 Index Numbers of Quantities (or Volume) 9.4 Further Concepts
9.4.1 Splicing Two Series of Index Numbers 9.4.2 Chain-Based Index Numbers
9.4.3 Using an Index to Deflate a Time Series 9.5 General Problems of Index Number Construction 9.6 Uses and Limitations of Index Numbers
9.7 Summary
9.0 OVERVIEW
This Unit introduces you to statistical tools called index numbers, which attempt to measure the magnitude of changes in any variable over time. Here, we shall be more concerned with changes in economic variables over time. The unit will cover the different types of price and quantity index numbers, the general problems of index number construction, interpretation, uses and limitations of index numbers. Chapter 8 of your textbook covers some of these topics. However, the different types of index numbers are not introduced in a proper order and also the different types of index number construction are not well defined (pp 158-164). This unit therefore, consists of a complete write-up of the topics covered in these pages in
your textbook as well as of other topics which are omitted in the chapter. We shall make special reference to these pages where necessary. Treatment of topics on pp 165-170 is quite satisfactory and, therefore, these topics are not re-written in the unit.
9.1 LEARNING OBJECTIVES
When you have successfully completed this Unit, you should be able to do the following:
1. Compute, interpret and compare the different types of price and quantity index numbers
2. Explain the importance of weights in an index number
3. Identify the main practical issues to be considered when constructing an index number 4. Change from fixed base to chain base and vice versa, splice and deflate an index
number series
5. Identify the uses and limitations of index numbers.
9.2 INDEX NUMBERS
As mentioned in the overview, index numbers are devices for measuring the magnitude of changes in a variable over time. Such changes could be in the price of commodities, in the quantity of goods produced, marketed, or consumed, or in such concepts as productivity, efficiency, etc. The comparisons may be between different time periods, between places, or between like categories. In many of these situations, the volume of data that has to be analysed is huge and also has other characteristics that you did not come across in data for averages. Index numbers are special types of averages which can make such masses of complex data more manageable and better understood, and thus enable us to compare different sets of data. Thus, we may have index numbers comparing the consumer prices in different years or in different countries, the volume of production in different years, the
This unit is mainly concerned with index numbers of prices and of quantities comparing changes over time. At first, methods of construction of index numbers of prices and of quantities are considered. We then introduce further concepts such as chain-based index numbers, splicing of index numbers and use of an index number to deflate a time series. You can read about splicing and deflating in your textbook (OJ). Finally, we deal with general problems of index number construction, and, uses and limitations of index numbers.
9.3 METHODS OF CONSTRUCTION OF INDEX NUMBERS
We shall consider methods of construction of price indices at first and later on show how quantity indices can be obtained similarly.
9.3.1 Index Numbers of Prices
To illustrate the construction and interpretation of index numbers of prices, we have used the data of example on p. 158 (OJ), which uses a list of three commodities.
Al Coholic throws a (rather unusual) party each Christmas for his friends. Details of prices and quantities of the three food and drink items purchased by him in 1992 and 1993 are as follows: Table 9.1 1992 1993 Commodity Price Po Quantity Qo Price Pn Quantity qn
Lager (per bottle) £1.00 40 £1.15 50
Crisps (per packet) £0.20 100 £0.27 90
The objective of A1 Coholic is to know the changes in the prices of these commodities taken as a whole in 1993 as compared with those in 1992. The time period that serves as the basis for comparison, is called the base period, whereas, the time period that is compared with the base period is called the current period. Thus, here 1992 is the base year and 1993 is the current year.
Note: The base period is sometimes indicated by calling that period as equal to 100. For example, here, 1992 = 100 will show that 1992 is the base year.
9.3.2 Two Approaches
There are two main approaches to handle the problem of determining the changes in the prices of a group of commodities taken as a whole in a given year as compared with those in another year:
One approach is to consider the change in the price of each commodity initially and then to try, in some way, to bring together these changes, by, for example, using an average.
The second approach is to consider the prices of all the commodities at one point in time and then relate them is some way, with those at the other point in time under consideration.
We shall now consider these two methods for the rest of this section.