Chapter 05

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 1

Chapter 5

Index numbers


Formula for a simple price index

Price index = pn/p0 x 100

where pn = price in year n

po = price in base year

A price index of 117 would indicate an increase of 17% relative to the base year.

A price index of 75 would indicate a decrease of 25% relative to the base year.


Table 1 Total value of exports (£ m)

Year Export Index (1992 = 100)1992 107 343 1001993 121 398 121398/107343 x 100 = 1131994 134 664 1251995 153 077 1431996 166 921 1561997 170 145 159

Source: Monthly Digest of Statistics, O.N.S.

Example: 1995 price has increased by 43 percentage points relative to 1992


Other index numbers

Retail Price Index RPI

FT Ordinary Share Index

Dow Jones Index

Basic wage rates index

Retail sales index

These are weighted averages for many different items.


Weighted aggregate indices

Items in the average index are weighted according to importance

Quantities may be used as weights

Index uses Price x Quantity (i.e. total cost or expenditure)

Base-weighted index – use base year quantities (Laspeyres)

Current-weighted index – use current year quantities (Paasche)


Base-weighted price index (Laspeyres’ index)

This is given by

100XyearbaseincostTotal

yearcurrentincostTotal

Where base-year quantities are used for both years

100 index Laspeyres’00

0

qp

qpn


Current-weighted price index (Paasche’s Index)

This is given by

100XyearbaseincostTotal

yearcurrentincostTotal

Where current-year quantities are used for both years

100 index sPaasche’0

n

nn

qp

qp


Example

` 1993 1999Number employed

Av salary (£000)

Number employed

Av salary (£000)

qo po poqo pnqo qn pn poqn pnqnSales 120 7.5 158 9Admin. 41 10 52 12.5Clerical 25 8 30 10Managerial 21 18 25 22.4Sum


Continued

qo po poqo pnqo qn pn poqn pnqnSales 120 7.5 900 1080 158 9 1185 1422Admin. 41 10 410 512.5 52 12.5 520 650Clerical 25 8 200 250 30 10 240 300Managerial 21 18 378 470.4 25 22.4 450 560Sum 1888 2313 2395 2932

Laspeyres index = 2313/1888 x 100 122.5Paasche index = 2932/2395 x 100 122.42


Retail Price Index

The RPI is used as a measure of inflation

It is a weighted average of a ‘basket of goods’ (around 350 items), updated regularly using the Family Expenditure Survey.

The RPI can be used for index-linking.

It can be used to deflate a series of values. This allows for inflation and looks at the underlying trend.


Deflating a series

Example:

Current year price deflated to 1992 prices

= Current year value x 1992 RPI__

current RPI


Table 1 Total value of exports (£m)

Year Exports Deflated series (to 1992)1992 107343 107343 1993 121398 121398 x 138.5/140.7 = 1195001994 134664 1294311995 153077 1421941996 166921 1513991997 170145 149620

Table 2 Annual average RPI (Jan 1987 = 100)198819941995 96 19971992 1993 1994 1995 1996 1997138.5 140.7 144.1 149.1 152.7 157.5


Graph to show deflation

Exports

100

110

120

130

140

150

160

170

180

1992 1993 1994 1995 1996 1997

Year

Ex

po

rts

in

£m

Exports (£m) Deflated exports


Comparison of indices

Indices give similar results if proportion of quantities for each item remain similar in both years.

Base-weighted (Laspeyres’ index) is most commonly used, e.g. RPI.


Advantages of Laspeyres’

Quantities in current year not required

Denominator is constant year to year

Indices can be compared year to year as well as to the base year

Disadvantages of Laspeyres’

Weights can quickly become out of date if quantities change

Education

Chapter 05