I keep being asked about the difference between the consumer price index and the retail price index. The immediate answer is that they include slightly different things. RPI includes the costs of housing (mortgage interest costs and council tax for example) while CPI does not.
However it isn’t that simple. If it was, we might have seen RPI fall below CPI as mortgage rates collapsed from 2008. The complicated bit – and the more relevant difference between the two – comes in the calculations. The RPI is an arithmetic mean – ie, 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 “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 difference of approximately 1% in the different indices. If the CPI were calculated as the RPI currently is, it would be about 1% higher than it is – and higher than the RPI. This is why the government likes to link the payments it makes (pensions and so on) to the CPI and the payments it receives (taxes and so on) to the RPI. More detail on all this here.