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Chapter 05 Chapter 05 Presentation Transcript

  • Chapter 5 Index numbers Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgra 1
  • 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 Palgra 2
  • Table 1 Total value of exports (£ m) Year 1992 1993 1994 1995 1996 1997 Export 107 343 121 398 134 664 153 077 166 921 170 145 Index (1992 = 100) 100 121398/107343 x 100 = 113 125 143 156 159 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 Palgra 3
  • 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 Palgra 4
  • 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 Palgra 5
  • Base-weighted price index (Laspeyres’ index) This is given by Total cost in current year X 100 Total cost in base year Where base-year quantities are used for both years ∑ p n q0 Laspeyres’ index = × 100 ∑ p0 q0 Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgra 6
  • Current-weighted price index (Paasche’s Index) This is given by Total cost in current year X 100 Total cost in base year Where current-year quantities are used for both years ∑ pn qn Paasche’ s index = × 100 ∑ p0 q n Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgra 7
  • Example ` 1993 Number Av salary employed (£000) qo Sales Admin. Clerical Managerial Sum po 120 41 25 21 1999 Number Av salary employed (£000) poqo 7.5 10 8 18 pnqo qn pn 158 52 30 25 poqn pnqn 9 12.5 10 22.4 Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgra 8
  • Continued qo Sales Admin. Clerical Managerial Sum po 120 41 25 21 poqo pnqo qn 7.5 900 1080 10 410 512.5 8 200 250 18 378 470.4 1888 2313 Laspeyres index = 2313/1888 x 100 Paasche index = 2932/2395 x 100 pn 158 52 30 25 poqn pnqn 9 1185 1422 12.5 520 650 10 240 300 22.4 450 560 2395 2932 122.5 122.42 Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgra 9
  • 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 Palgra 10
  • Deflating a series Example: Current year price deflated to 1992 prices = Current year value x 1992 RPI__ current RPI Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgra 11
  • Table 1 Total value of exports (£m) Year 1992 1993 1994 1995 1996 1997 Exports 107343 121398 134664 153077 166921 170145 Deflated series (to 1992) 107343 121398 x 138.5/140.7 = 119500 129431 142194 151399 149620 Table 2 Annual average RPI (Jan 1987 = 100)19881994 1995 96 1997 1992 1993 1994 1995 1996 1997 138.5 140.7 144.1 149.1 152.7 157.5 Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgra 12
  • Graph to show deflation Exports 180 Exports in £m 170 160 150 140 130 120 110 100 1992 1993 1994 1995 1996 1997 Year Exports (£m) Deflated exports Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgra 13
  • 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 Palgra 14
  • 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 Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgra 15