A lot has been written about the impact that a change from RPI to CPI would have on pension scheme members, the financial markets and the wider economy. There has also been much comment on the differences between the calculation of these indices. But which is the better measure of inflation?

This is not the first time that indices have been compared. I have done some work in this area in relation to longevity indices, but my research was itself based on an earlier paper by Jeffery Bailey. In 1992, peer group benchmarks were still widely in use. Following a peer group benchmark involves driving your investment strategy based on what everyone else, on average, has just done – not a particularly effective strategy. Frustrated by the adherence of investors to such approaches, Bailey arrived at a series of characteristics that a good benchmark should have. These criteria can be summarised as:

  • unambiguous – components and constituents should be well-defined;
  • investable – it should be possible to buy the components of a benchmark and so to track it;
  • measurable – it should be possible to quantify the value of the benchmark on a reasonably frequent basis;
  • specified in advance – it should be known by all participants before the period of assessment has begun;
  • appropriate – it should be consistent with an investor’s style and objectives; and
  • reflective of current investment opinion – it should contain components about which the investor has opinions (positive, negative and neutral).

Clearly one does not invest in inflation in the same way as one invests in stocks and shares, but it is worth seeing how the Retail Price Index and Consumer Price Index stack up on this basis.

Are RPI and CPI unambiguous? As far as they can be, yes. The raw ingredients for both are the prices of various goods and services, with prices being collected by a large team of researchers. These researchers simply go to the shops, write down the prices of a the goods and services in the index, and report back to base. For some items like TV licences and rail fares the data are instead collected centrally. Could the method be made more objective? Probably, by having an automatic transfer of data from retailers to the Office for National Statistics; could it be made more objective at a reasonable cost? Probably not.

Are RPI and CPI investible? This is an interesting one. You could argue that a good index should mean that if you to buy a basket of goods, hold onto it for a month and then sell it again, the amount by which the value of the basked has increased should be the same as the the increase in the price index. This implies that an arithmetic index should be used, where you simply add all the prices together, weighted by the amount of each item in the basket. The is the method used to calculate RPI. Of course, it is not possible to buy and hold a basket of goods. Apart from the fact that fresh produce would go off, how do you buy and hold a haircut? However, the arithmetic approach is intuitively appealing.

The same method is used to calculate CPI.

Hold on, isn’t CPI a geometric index? In fact, isn’t that one of the main issues with CPI? Well, there is a geometric element to the calculation, but only at a basic level. Under RPI, when the various prices for a particular good or service have been collected, a straight arithmetic average is taken; under CPI, the geometric mean is taken for these prices. However, the CPI itself uses a weighted arithmetic average of these geometrically averaged prices, in the same way that the RPI aggregates the arithmetically averaged results.

The reason prices for a particular good or service are averaged geometrically rather than arithmetically is because price volatility can lead to the result being unrealistically inflated under the arithmetic approach. One way of thinking of this is the geometric result assumes that people will switch products in response to price changes whereas the arithmetic result assumes that no change will be made. The reality is probably somewhere between the two. There are some brands I would always choose, whereas for some products I’ll just follow the two-for-one deals. However, for items such as council tax where switching to a cheaper alternative would involve moving house, the geometric approach could be seen as unfair.

Are RPI and CPI measurable? Well, yes. Given the raw data on prices, it is straightforward – if time-consuming – to calculate and track both.

Are RPI and CPI specified in advance? Again, an east one – the baskets of goods are known at the start of each calculation period, so constituents are not altered to artificially lower either index.

Are RPI and CPI appropriate and reflective of consumer habits? Ok, I’ve cheated and aggregated these last two criteria into one, but together they form an important question. It could be rephrased as: do the baskets of goods in the two indices reflect what the users consume? This is a bit of a moving target, as the constituents of both can change. However, it is interesting to consider some of the current similarities and differences. Both RPI and CPI try to cover only consumption, not investment. This means that contributions to pension plans are excluded, as are mortgage capital repayments. National insurance and income tax are also excluded, as taxation is not regarded as consumption.

The RPI includes vehicle tax and many housing costs, whilst the CPI does not; conversely, the CPI includes various investment charges, university accommodation fees and foreign students’ university tuition fees, all of which are excluded from the RPI. Of these items, housing costs will be the main source of difference between the two indices – the impact of foreign students’ university tuition fees, for example, must be marginal. From the point of view of a pensioner, this will often mean that CPI is more appropriate.

So in conclusion, the CPI doesn’t look like an entirely unreasonable index to use for calculating pensioner benefits. Does this mean that the proposed change from RPI to CPI should go ahead? Not necessarily. The impact of such a change will be wide-ranging and, potentially, administratively complex. There is also the small issue of people signing up for one benefit and receiving another. However, it is important to recognise that whilst a change to CPI from RPI might be unfair, CPI itself is not inherently a bad measure of prices.