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# Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd1 Chapter 5 Index numbers.

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Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd1 Chapter 5 Index numbers

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd2 Formula for a simple price index Price index = p n /p 0 x 100 where p n = price in year n p o = 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 Ltd3 Table 1 Total value of exports (£ m) Year Export Index (1992 = 100) 1992 107 343100 1993 121 398121398/107343 x 100 = 113 1994 134 664125 1995 153 077143 1996 166 921156 1997 170 145159 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 Ltd4 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 Ltd5 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 Ltd6 Base-weighted price index (Laspeyres index) This is given by Where base-year quantities are used for both years

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd7 Current-weighted price index (Paasches Index) This is given by Where current-year quantities are used for both years

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd8 Example

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd9 Continued

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd10 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 Ltd11 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 Palgrave Publishers Ltd12 Table 1 Total value of exports (£m) YearExports Deflated series (to 1992) 1992107343107343 1993121398121398 x 138.5/140.7 = 119500 1994134664 129431 1995153077 142194 1996166921151399 1997170145149620 Table 2 Annual average RPI (Jan 1987 = 100)19881994 1995961997 199219931994199519961997 138.5140.7144.1149.1152.7157.5

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd13 Graph to show deflation

Essential Quantitative Methods 2nd edn © Les Oakshott 2001 Palgrave Publishers Ltd14 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 Ltd15 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

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