Measuring Inflation Contents

Appendix 4: Chained and direct Carli indices

The Royal Statistical Society, in support of their argument that the chained version of the Carli index suffers from ‘price bouncing’ but the direct index does not, submitted the calculations below.

Table 3: Hypothetical example given by the Office for National Statistics185

Period 1

Period 2

Period 3

Product A

10.00

12.50

10.00

Product B

20.00

10.00

20.00

Table 4: Direct Carli calculation

Price relatives

Period 2 / Period 1

Period 3 / Period 1

Product A

1.25

1.00

Product B

0.50

1.00

Index overall

0.88

1.00

Table 5: Chained Carli calculation

Price relatives

Period 2 / Period 1

Period 3 / Period 2

Product A

1.25

0.80

Product B

0.50

2.00

Arithmetic mean of relatives

0.88

1.40

Index overall

0.88

1.23

Table 6: Jevons index

Period 1

Period 2

Period 3

Geometric mean of prices

14.14

11.18

14.14

Month to month movement

0.79

1.26

Index

0.79

1.00

Source: Written evidence from Royal Statistical Society (RPI0025)



185 Office for National Statistics, ‘Shortcomings of the Retail Prices Index as a measure of inflation’ 8 March 2018: https://www.ons.gov.uk/economy/inflationandpriceindices/articles/shortcomingsoftheretailpricesindexasameasureofinflation/2018–03-08 [accessed 21 December 2018]




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