A Practical Introduction to Index Numbers

Jeff Ralph, Rob O'Neill, Joe Winton

• Publisher: Wiley
• Year: 2015
• Print ISBN: 9781118977811
• eBook ISBN: 9781118977798
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

This book provides an introduction to index numbers for statisticians, economists and numerate members of the public. It covers the essential basics, mixing theoretical aspects with practical techniques to give a balanced and accessible introduction to the subject. The concepts are illustrated by exploring the construction and use of the Consumer Prices Index which is arguably the most important of all official statistics in the UK. The book also considers current issues and developments in the field including the use of large-scale price transaction data.

A Practical Introduction to Index Numbers will be the ideal accompaniment for students taking the index number components of the Royal Statistical Society Ordinary and Higher Certificate exams; it provides suggested routes through the book for students, and sets of exercises with solutions.

Chapter 1
Introduction

1.1 What is an index number?

The simplest description of an index number is that it is a measure of change. Consider the data in Table 1.1, which shows the total value of retail sales¹ for Great Britain between 2005 and 2008 presented in two ways, firstly, as values in billion pounds, and secondly, scaled so that the value in 2005 is set to be 100.

Table 1.1 Value of retail sales 2005–2008 for Great Britain.

	Value of retail sales (£bn)	Value relative to sales in 2005 (2005 = 100)
2005	281.450	100.00
2006	292.110	103.79
2007	303.621	107.88
2008	321.178	114.12

Source: Office for National Statistics (Time series of retail sales data are available from the ONS website http://www.ons.gov.uk/ons/rel/rsi/retail-sales/july-2013/rft-rsi-poundsdata-july-2013.xls; series ValNSAT).

The idea behind representing the time series of the values of sales in a scaled form is to make the degree of change readily apparent. The process of creating values in the third column is a simple one. Firstly, we choose a time period as the reference time period with which we want to compare the change; in this case, we have chosen 2005 as the reference (or base) time period. The index number series is then scaled to be equal to 100 for this reference period; the same scaling factor is then applied to the values of sales for other years. We explain how to do this in detail in Chapter 2.

The values for the scaled series are set to be around 100, as this is judged to make the degree of change clearest; the scaled values are called index numbers. Representing the time series in this way makes comparison easy. For example, the percentage change in retail sales between 2007 and 2005 can just be read from the index number for 2007 – it is 7.88%. Note that although the scaling process changes the numbers, it does not alter the percentage differences. Chapter 2 shows how to convert the percentage change from an index series back to values; for example, if we want to calculate how much money the change of 7.88% in this series represents.

By creating an index number representation of the time series of retail sales values, we have gained a more direct representation of change. In doing so, we have lost the actual monetary values; however, frequently the focus is primarily on the change in the level of the series rather than on the actual amount sold in billion pounds.

1.2 Example – the Consumer Prices Index

A different example of an index number series is provided by the Consumer Prices Index (CPI). This is a measure that tracks the movement in the general level of prices of consumer goods and services.

Table 1.2, taken from the CPI Statistical Bulletin for September 2013, shows index numbers representing the general level of prices for each month from September 2012 to September 2013,² where the index value has been set to be 100 in 2005. The index number represents the general level of prices in any given month. The change between the level of prices in any given month and the level of prices in 2005 is easily found by referring to the index number. For example, in September 2012, we can see that prices had increased by 23.5% from 2005.

Table 1.2 CPI values, 1- and 12-month inflation rates: September 2012–2013, United Kingdom.

		Index (UK, 2005 = 100)	1-Month rate	12-Month rate
2012	Sep	123.5	0.4	2.2
	Oct	124.2	0.5	2.7
	Nov	124.4	0.2	2.7
	Dec	125.0	0.5	2.7
2013	Jan	124.4	−0.5	2.7
	Feb	125.2	0.7	2.8
	Mar	125.6	0.3	2.8
	Apr	125.9	0.2	2.4
	May	126.1	0.2	2.7
	Jun	125.9	−0.2	2.9
	Jul	125.8	0.0	2.8
	Aug	126.4	0.4	2.7
	Sep	126.8	0.4	2.7

Source: Office for National Statistics.

Table 1.2 also contains the per...

Table of contents

• Cover
• Title Page
• Copyright
• Table of Contents
• Preface
• Acknowledgements
• Chapter 1: Introduction
• Chapter 2: Index numbers and change
• Chapter 3: Measuring inflation
• Chapter 4: Introducing price and quantity
• Chapter 5: Laspeyres and Paasche indices
• Chapter 6: Domains and aggregation
• Chapter 7: Linking and chain-linking
• Chapter 8: Constructing the consumer prices index
• Chapter 9: Re-referencing a series
• Chapter 10: Deflation
• Chapter 11: Price and quantity index numbers in practice
• Chapter 12: Further index formulae
• Chapter 13: The choice of index formula
• Chapter 14: Issues in index numbers
• Chapter 15: Research topics in index numbers
• Appendix A: Mathematics for index numbers
• Appendix B: Choice of index formula
• Appendix C: Glossary of terms and formulas
• Appendix D: Solutions to exercises
• Appendix E: Further reading
• Index
• End User License Agreement