1. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Chapter 7: Index Numbers

2. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Objectives Describe the concept of an index number Explain why they are calculated Calculate simple index numbers Time-align index numbers Calculate Laspeyres indices Calculate Paasche indices Describe at least one published index Find published data and series

3. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage What is an Index Number? It is a means of making comparisons It is always related back to the base year The base year has a value of 100 It can be used for just one set of figures It can also be used to amalgamate several sets of figures It can allow for the different relative importance of items in the index series

4. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Why use them? Index numbers allow you to compare very large numbers quickly and easily Percentage changes from the base year can be found at a glance Some are well known: For example, the Retail Prices Index this is linked to increases in various benefits

5. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage A Single Set of Figures YearPrice per bottle 11.50 21.62 31.69 41.79 52.05 Suppose we have the price of bottled beer over a 5 year period The first task is to pick a base year Here we will choose Year 1 Index Series 100 108 112.7 119.3 136.7 this is given a value of 100 Other values are found by dividing the price by the base year price and multiplying the result by 100 eg. Year 2 is (1.62/1.50)*100 = 108

6. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Time-aligning Series When we want to compare the changes in different index series, it will be much easier if they all start at the same point in time. Since this is often not he case, we need to modify a series to align it with another one, For example: YearIndex of WagesIndex of Prices 1100120 2104123 3110127 4117134 5121138 6128140 7135145

7. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Time-aligning Series (2) If we choose Year 1, then we need to change the 120 for Price to 100 We can do this by dividing by 120 (the value in the chosen base year) and multiplying by 100 We then divide each of the other Price index numbers by 120 and multiply be 100 N.B. We use multiplication/division since the figures are relative to the base year The simplest way to do the sums is on a spreadsheet

8. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Time-aligning Series (3)

9. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Comparisons of Groups of Figures Rarely do we consider just one set of figures, say the price of a single item However, when we combine various items, we must make allowances for the fact that some will be more important than others. We often use the quantities purchased to weight the prices in calculating an index number Other systems, of course, can be devised to weight items in an index series

10. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Base-weighted Indices ItemPrice (Yr1) Quantity (Yr1) Price (Yr2) Price (Yr3) Chips272.12.2 Beer4204.64.9 Ciggs849.210.5 An advantage of base-weighting is that less data needs to be collected than other systems This makes it cheaper to construct sincewe only need price and quantity information for a single year. For example:

11. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Base-weighted Indices (2) To take account of relative importance of items, we can multiply the Prices by the Quantities. This can be done on a spreadsheet Note that we create 3 extra columns, one for each year

12. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Base-weighted Indices (3) A base-weighted index is also called a Laspeyres Index The formula to help you remember what to do is: Where P n is the price in the current year, and P 1 is the price in the base year (Similarly for the quantities)

13. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Current Weighted Indices Whilst base-weighted are simple, they cannot take account of changes in amounts bought over time To do this we need to get both price and quantity information for every year ItemPrice (Yr1) Quantity (Yr1) Price (Yr2) Quantity (Yr2) Price (Yr3) Quantit y (Yr3) Chips272.1102.210 Beer4204.6254.930 Ciggs849.2010.50

14. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Current Weighted Indices (2) 142122 80115147 3200 Total 126136169 Item P1Q1P2Q2P3Q3 Chips Beer Ciggs Firstly we need to find actual amounts spent in each year Multiply Price by Quantity for each year P1Q2P1Q3 20 100120 00 Total 120140 Item Chip s Beer Cigg s Then we can find how much would have been spent in each year using base year Prices and current year quantities

15. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Current Weighted Indices (3) Now we are in a position to compare the two sets of figures to create the index numbers For Year 2: For Year 3: A current-weighted index number is also called a Paasche index A formula to help you remember is:

16. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Retail Prices Index Probably the most widely used published index Monitors the prices of hundreds of items Wide geographical spread Details on the web site http://www.statistics.gov.uk

17. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Conclusions Index numbers always make comparisons back to a base year They help to compare large numbers They can group items together, even if they are measured in different ways Often used for published data