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

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.

• Dr Bob

Maybe the policy link to CPI reflects anxiety over how quickly RPI can turn negative?! (As in 2009: http://www.bbc.co.uk/news/10612209)

Will this look like a policy blunder when both measures finally turn negative again? Or an act of self-interest by public sector workers?!

Keep up the good work on Gold. With a bit of luck, Mr King will be dissuaded from holding off deflation for much longer and finally give us what we deserve.

Have you looked at M4 “growth” rates recently btw? (http://www.bankofengland.co.uk/statistics/bankstats/current/index.htm#1)

Can we please have an article about where the BOE’s gilt income is going? Are they helping the money supply shrinkage along at present?

What exactly are they doing with the money? Setting fire to it? What’s the opposite of “printy, printy”? “Deletey, deletey”?

• Jon

…both measures have been manipulated to meet government requirements – remember Gordon Brown’s “harmonisation with European methods” ? Utter tosh to make us think we have a lower level of inflation than is really the case.

Problems with the current RPI are that

a) it is self fulfilling as it includes mortgage interest payments; higher[lower] interest rates=higher[lower] RPI = higher[lower] interest rates… but,

b) it still doesn’t include house prices which interest rates should’ve been controlling.

• Critic Al Rick

The Govt consists of, amongst other entities, a ‘cartload of crafty monkeys’. Amongst its arsenal of tools for supposedly surreptitiously cheating Joe Public are certain ‘fudge’ tools which ‘work’ upon specific items (benefits and taxes) to favourably engineer them over the years; favourable in the context that the monkeys (theoretically) have more and more money to squander as the years go by.

RPI and CPI are ‘fudge’ tools. CPI, for the present at least, in the context of Treasury payouts is a bigger ‘fudge’ than RPI. But expect them both, one day, to be superceded by an even bigger ‘fudge’ for the calculation of such payouts.

Another devious tool, arguably the most abhorrent in their arsenal, is called Inflation. The monkeys would probably like Joe Public to see Inflation as a tonic to an ailing economy. But it isn’t, it’s a slow release poison which will eventually ‘kill’ Joe Public’s Freedom.

And as for GDP, don’t get me started!

• Pensioner

Critic Al Rick is right about fudge factors. It’s not generally known but since 2003 the Office for National Statistics has quietly introduced what are known as “hedonic regression algorithms” in the calculations for the costs of certain items in the “shopping basket” for both the RPI and the CPI. The net effect is of course to lower both indices slightly which the government loves because it not only makes the indexes closer to the target for inflation but also saves the government money.

• Alberto

“But the real advantage to the government of using a geometric mean is that it is always below or equal to the arithmetic mean.”

The above is tru only if the averages are calculated for the SAME numbers. If you put different nubers everything could be.

Is the geometric average of 3 and 4 below the arithmetic average of 1 and 2….?

• Joe

@ Alberto

I’m fairly sure that Merryn is saying to that for a given set of numbers the geometric mean is less than or equal to the arithmetic mean. So if the CPI were worked out using the arithmetic mean it would tend to be a higher figure.

• Ed

The example on the ONS website is for two prices which start at 100 and one increases by 20% and the other falls by 20%. The arithmetic and geometric means are 102.5 and 100 respectively.

So if you are a pensioner, and your bills change from £200 (100+100) to £205 (125+80) your cost of living goes up but you get no extra money.

This is a disgraceful trick and if continues for decades the differences will be very significant. Thank you Merryn for pointing this out.

• David Quinn

The geometric mean(GM) is used because it is supposed to model the notion that as prices rise people can substitute lower price alternatives without any loss of quality. All the examples given of the sort of substitutions which can be mad are rubbish. The quality of the substitutes is always less. Trying to achieve such substitution reliably and consistently in a world of supermarkets is virtually impossible so the government’s (and the economists’ who devised this idea) claim is clearly nonsense. And the Jevons formula on which this idea is based does not actually say this. Basically this, to paraphrase Al Gore, is a convenient untruth. Even if the government fixes the omission of housing costs and Council Tax in CPI the GM effect will keep robbing most of us of 0.7% in real terms year after year. If you are 20 today and are lucky enough to have a pension it will be worth up to 50% less in real terms by the time you pick up. This is not just utterly dishonest it is wholly immoral.

• Toby

It is certainly mathematically true that the geometric mean is always less or equal to the arithmetic mean for any set of non-negative numbers.

I can see no logical reason to use the geometric mean. The inequality is particularly significant if you get one item in the basket which, say increases by 1000%. So maybe the argument is that it protects the index from going mad when just one item (eg the cost of chocolate) goes unexpectedly through the roof.

My gut feeling is that governments will always try and con the public with these kinds of mathematical tricks. Despicable, really.

• Critic Al Rick

@ 10. Toby

And it’s such despicable deviousness from our supposed leaders, albeit relatively low key compared to the blatant disrespect emanating from Banksters, that sets a bad moral example to the rest of Society.

Never mind the ‘n’th root of the product of ‘n’ quantities; therein lies the root of the demise, in all regards, of the West; probably history repeating itself. For the power of greed (and fear) can overcome sanity.

The ‘host’ has all but ‘got its back against the wall’; if it overcame the fear and acted rationally, it would ‘turn like a provoked worm’ on the ‘parasites’. A good place to start would be Westminster; a veritable ‘loss leader’!

Have I strayed off-topic? – ‘and why it matters’. No, I don’t think so.

• Purse String

The real inflation I witness is in the shrinking packets in the supermarkets eg. 800ml now instead of a litre etc. and still charging the same price. If the ONS use shelf prices the picture will seem steady (suits Govt) but the consumer is paying 20%more. As I understand it, items in the ONS basket are given ‘weightings’ in order of importance and do not consider the weights and measures side of things.
The ONS may crunch numbers on this on the quiet but I guess it would be too scary for the Govt to use or reveal to Joe Public. It is also difficult to take the current RPI figures seriously anyway whilst the markets/currencies are in such turmoil. The ONS do produce other indices (factory gate prices etc.) for the brave economists out there and I think a wider range of data helps.
Finally, I wonder how the housing costs (mort int) is calculated within RPI since it is the taxpayer/consumer that bailed out the banks ? Do they factor that in?

• CKP

Good point well made, not understood by 99% of people and journalists. Housing costs actually make up a fairly low component of RPI, the formula difference explains most of the disparity.
A housing crash in the UK is unlikely to mean a large fall in RPI, as rising interest rates will offset this.

• SimonH387

Any further interest rate cuts from 0.5% will make very little difference. What Gordon Brown should have done was raise interest rates in 2004. Instead he changed the Inflation rate standard from RPI to CPI. Had RPI remained in place after 2003, interest rates would have risen and the borrowing would have been slowed down in 2004 not 2007. How Brown has escaped blame despite controlling the Treasury from 97 to 2010 is beyond me