The Retail Price Index and the Consumer Price Index – Concerns of the Royal Statistical Society
1. The Royal Statistical Society (RSS) has had concerns about the RPI and the CPI for some while and has raised these on more than one occasion.1,2 We do not consider either index to be ideal for the various purposes for which they are put. The different estimates the indices give of inflation have clearly undermined confidence, particularly in the CPI.
2. Our main concerns are twofold: the difference in coverage, notably the exclusion from the CPI of owner occupiers housing costs and certain other variables; and the difference in aggregation formulae used in the compilation of the indices; this gives rise to what is known as the “formula effect” (see appendix). In our view, there is no good statistical reason for either of these differences.
3. Together these two factors result in the rate of inflation shown by the CPI being substantially lower, on average, than that of the RPI. Analysis by the Office for Budgetary Responsibility (OBR) (pdf format) published last November suggested that over the long term this would amount to CPI annual inflation being 1.3 to 1.5 percentage points lower on average than that shown by the RPI. This implies, for example, that after ten years a pensioner whose pension was uplifted by RPI would have a pension around 15% higher than someone who started on the same pension but with an uplift determined by CPI.
4. The lesser part of the OBR difference – around 0.5 percentage points – is accounted for by owner occupier housing costs and related matters. The Office for National Statistics (ONS) has a well-advanced programme which aims to include these in the CPI from early 2013. However, they will not be measured in the same way as in the RPI (see appendix) so it is possible that some differences will remain.
5. The formula effect is larger, around 0.8 to 1.0 percentage points on average, according to the OBR’s analysis. It is pernicious when the indices are used to uplift pensions, wages or business contracts since mathematically it always works in the same direction. Deciding which mathematical formula is better is not a simple question. Among other issues it depends on assumptions made about consumer behaviour: how consumers react to changes in prices of different brands or between different shops; and how in some cases they spur such changes through their preferences (eg obliging retailers to discount slow-selling items). It is also affected by survey design. It is probable that the RPI overestimates inflation as experienced by the average consumer. It is possible that the CPI underestimates it.
6. The Office for National Statistics now has a research programme into the reasons for the formula effect, and into which formula is most appropriate for different types of goods and services. It is a complex and multi-faceted problem which will not be solved quickly but it is imperative that it is carried out properly and as swiftly as possible consistent with the need to investigate fully. As results from this research become available the compilation of the CPI should be adapted; we believe this is the ONS’s intention.
7. The RSS appreciates that there are constraints on the compilation of the RPI arising from terms in the prospectuses for early index-linked gilts. However the RPI should also be improved to the extent possible following the research results. The CPI is currently effectively the UK version of the Harmonised Index of Consumer Prices (HICP) which is compiled on EU standards; however there is no obligation on the UK to use this as the headline index and most EU countries do not.
8. Statistics should be compiled according to user needs. What has not yet been done but is urgently needed is a full assessment of the different uses to which consumer inflation measures are put and therefore what indices are needed (eg is it appropriate to have different indices for different household types).
9. It is crucial that a measure as important as a consumer price index enjoys public confidence. The CPI clearly does not. The various initiatives described above need to be properly carried out and the results implemented before confidence can be built.
The formula effect
The formula effect is the term used for the difference in the inflation rates shown by the two indices that is due to the ways that they are calculated.
Specifically this arises from the use of different methods of constructing the two indices at the first stage of aggregation, when individual price quotes are combined to calculate indices for individual items. The RPI uses two separate forms of an arithmetic mean (adding n items together and then dividing by n) for this purpose. The CPI uses the geometric mean (multiplying n items together and then taking the nth root), for the majority of items.
Mathematically the form of arithmetic mean used for a number of items in the RPI will always give an equal or higher rate of inflation than the geometric mean. The difference increases with the variability of price movements. Clothing, where items are not uniform and price movements can vary substantially, accounts for the largest share of the formula effect. The ONS’s current work is focused on clothing.
Measuring owner occupier housing costs
It has been difficult to obtain consensus within the EU on the treatment of owner occupier housing costs which is why these are currently excluded from the Harmonised Index of Consumer Prices which the ONS uses as the UK’s CPI.
The RPI includes mortgage interest payments, house depreciation and Council Tax, which the CPI currently excludes. Under current plans, the ONS is investigating two ways of covering owner occupier housing costs in the CPI: the rental equivalence approach which would measure the notional rent that owner occupiers would pay if they rented their property, or the net acquisitions approach which is essentially the cost of buying and maintaining a house but excludes the cost of land.
1 RSS President to Chair of UK Statistics Authority, 25 August 2010
2 RSS Vice President to Chair of UK Statistics Authority, 22 February 2011