A Price Index Peculiarity

Inflation is a current worry in the UK, and the method of measuring it has also been attracting attention because the Coalition decided last year to use the CPI (Consumer Price Index) instead of the RPI (Retail Price Index) as the basis for increasing various benefits and pensions.

Every month the Office for National Statistics (ONS) publishes a bulletin of consumer price data. The figures which get the most media attention are not the actual indices but the percentage changes over 12 months eg “Annual inflation as recorded by the retail prices index (RPI) stands at 4.8 per cent in December, up from 4.7 per cent in November.”

(Boring bit) The percentage change in month “m” over the same month a year ago “m-12” is simple to derive from the indices by the formula:

( Index for month m – Index for month (m-12) / Index month (m-12) ) x 100

or to put it more simply, if the index is 220 now and was 200 a year ago, the percentage change is:

(220 - 200) / 200 x 100 = 10%

Table 2 of the ONS Statistical Bulletin December 2010 gives the RPI and CPI data for the last 36 months. Using the ONS index data and the formula above, the percentage changes for the RPI for the last 24 months are easily calculated using Excel – not surprisingly these come out to be the same as the figures printed in the Bulletin.

Now here’s the odd thing. As the table below shows, for the CPI data eight times in the last 24 months the ONS figure is 0.1% higher than the calculated one. For these cases the calculated percentage is also shown with a second decimal place – which doesn’t provide any explanation.  If anyone can cast some light as to why this is happening with the CPI but not the RPI, please add a comment!

ADDENDUM: For the explanation see my post on 3 April 2011: http://bit.ly/i4mV6g