Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 1
Chapter 5
Index numbers
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 2
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.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 3
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
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 4
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.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 5
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)
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 6
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
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 7
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
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 8
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
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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
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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.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 11
Deflating a series
Example:
Current year price deflated to 1992 prices
= Current year value x 1992 RPI__
current RPI
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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
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 13
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
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 14
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.
Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd 15
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