## RPI v CPI – the evidence so far; (Jon&Con)

This article is from Jon Spain and Con Keating, intellectual powerhouses of this blog. It asks us took again at the relationship between RPI and CPI

Financial services professionals commonly state that, over the long term, RPI increases will exceed CPI increases by 1% pa. Having run www.ukrpi.com for 12 years (to be updated further soon), we’ve often wondered about that and we thought we’d look at the evidence again.

The UK CPI has been available since 1975 and we have looked at periods ending at the end of each calendar year, until 2021. Although CPIH (available since 1989) has become HMG’s preferred measure, the differences between CPI and CPIH are not significant. The numbers shown below are the per annum increase differences between RPI and CPI.

Comparing RPI with CPI over 1 year, the average has been 0.73%, with a standard deviation of 1.02%. As it occurs at the 60th percentile, it is not unreasonable to suggest that the expected difference could be as high as 1%.

However, comparing RPI with CPI over 15 years, the average has been 0.72% (virtually the same as over 1 year), with a standard deviation of 0.10%. A value of 1% would be 2.84 standard deviations away from the mean, which corresponds to a likelihood of 1 in 200, namely highly unlikely. Hence, 1% really cannot be taken as a best estimate.

Con Keating & Jon Spain

## About henry tapper

Founder of the Pension PlayPen,, partner of Stella, father of Olly . I am the Pension Plowman
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### 7 Responses to RPI v CPI – the evidence so far; (Jon&Con)

1. Peter Tompkins says:

I would be interested to see the maths behind this. With only 46 years of CPI data there are only 3 independent periods of 15 years to look at so I can’t see how the s.d. for the 15 year calculation should be so tiny.

Although this is arcane it does matter for DB plans with liability matching to RPI stocks where you have CPI pension increases.

2. Dr+Robin+Rowles says:

I always told by statisticians that the main reason for prefering CPI over RPI was that the CPI calculation was more mathematically rigorous than that for RPI as apparently if you work backwards from a CPI figure using the reverse of the CPI calculation method you will calculate the the previous figures, but not if you do the same with the RPI and RPI methodology. Presumably if DB are to be forced to change to CPI it will make them more financially robust.

• Dennis Leech says:

What you are saying is (the frequently made claim) that RPI fails the time reversal test whereas CPI passes it. That is not actually true. It is a fallacy. Neither index passes the test because they are both Laspeyres type indices.

The point you are making only matters at the elementary stage where the prices for the elementary aggregates (that are combined in the second, Laspeyres stage) are computed: CPI uses a geometric mean, which cannot exceed the arithmetic mean used for RPI.

The whole argument is very weak and greatly overstated in my view. It has not been demonstrated that RPI overstates inflation and that CPI is more accurate.

See my paper ‘What’s Wrong with the Retail Prices Index Anyway?’ presented at ESCoE Conference on Economic Measurement 2021 11-13 May 2021.

• Dennis Leech says:

Your statement “…if you work backwards from a CPI figure using the reverse of the CPI calculation method you will calculate the the previous figures, but not if you do the same with the RPI and RPI methodology.” is not true as a generalisation. First, as I explained in my earlier comment, the criticism is equally valid for CPI as RPI because they are both of the Laspeyres-type. Second, if the prices of all goods sampled move equiproportionally both indices are identical. The issue you refer to is valid when the prices move by varying proportions. That is of course important but it is an empirical question how much difference it makes. Most of the toy examples that have been used to demonstrate this point involve assuming some extreme price movements in opposite directions for different goods.

3. The formula effect increased significantly in 2010 (due to a change in the collection of clothing prices) so you cannot extrapolate more historic trends into the future

4. John Mather says:

Neither take into account the effect of inflation on the income band of the individual as can be seen from the recent cost of energy.

https://www.ft.com/content/7486d44c-3b4f-4e9f-9e78-4025f74d4ce4

The UK needs to address productivity or continue to rob Peter to pay Paul

5. con keating says:

This message is from Jon

I would like to begin by thanking Peter for his comments, and apologising for the delay in responding which was due to illness. Yes, I agree that there can be only 3 fully independent periods of 15 years within fewer than 60 years annual data. However, for modelling inflation over 15 years, one would want figures which are interdependent with those for other periods, just as in real life. Further, each period of 15 years represents one possible outcome, which actually happened, Accordingly, I consider that it is entirely appropriate to take each interlinked period of 15 years, as I have done. The spreadsheet is available by email from either me or Con Keating.