The difference between CPI and RPI inflation – and why it matters

I keep being asked about the difference between the consumer price index (CPI) and the retail price index (RPI) measures of inflation. The immediate answer is that they include slightly different things, and – the more relevant difference between the two – they are calculated in different ways.

The RPI is an arithmetic mean; the prices of everything to be included in it ar­e simply added up and divided by the number of items. The CPI is a geometric mean; it is calculated by multiplying the prices of all the items together and then taking the nth root of them, where “n” is the number of items involved.

Look on the ONS site and you will see that it really isn’t mad for the RPI. It lost its status as a national statistic back in 2013 and the latest release on the matter is pretty clear that it is considered “a very poor measure of general inflation at times greatly over estimating and at other times underestimating changes in prices and how these prices are experienced.”

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The ONS also reckons that it is more likely to overstate than understate inflation “although it is impossible to be precise about the extent of any upwards bias.”

It is also the case, says the ONS, that “an advantageous property of the geometric mean is that it can better reflect changes in consumer spending patterns relative to changes in the price of goods and services.” That may be so, but the real advantage to the government of using a geometric mean is that it is always below or equal to the arithmetic mean.

So much so that the so called “formula effect” tends to produce a significant difference in the different indices, with the RPI usually ending up between 0.7 and one percentage point higher than other measures and sometimes rather more: in November CPI was 10.7% and RPI was 13.5%. That’s a meaningful difference and might go some way to explaining why the government still uses RPI to calculate all sorts of things – despite it being of no use to the ONS as a national statistic.

Look to the list of things CPI is considered useful for and you will mostly see that it involves calculating rises in payments from the government to the public (jobseekers allowance, the state pension, universal credit, housing benefit and personal independence payments for example).

Look to the list of things that use generally significantly higher RPI and you will see they mostly involve the calculation of rises in payments from the public to the government (interest on student loans, alcohol duty, tobacco duty, car tax and air passenger duty for example). Who could have guessed it would end up that way around?

According to the latest inflation data, published on 14 December, CPI rose by 10.7% in the 12 months to November 2022, down from 11.1% in October. Meanwhile, the CPIH index (which includes owner occupiers' housing costs) rose by 9.3% over the same period, down from 9.6% in October.

The slight easing was driven largely by motor fuels, says the ONS, with rising prices in restaurants, cafes and pubs making the largest upward contribution.