RPI vs CPI: the row goes on

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Two new contributions to the argument over how the UK measures inflation show that the issue is far from dead. Arcane the argument may be, but its effects are not.  

The decision by the Coalition Government in June 2010 to change the way benefits and public sector pensions are uprated from the Retail Price Index (RPI) to the Consumer Price Index (CPI) means that millions are affected – and, in general, disadvantaged – by a change that has also left many statisticians uneasy.

A excellent summary of the issue, written by Jill Leyland for the Royal Statistical Society, is available on the Significance website. The nub of the issue is that inflation measured by CPI is generally lower than that measured by RPI and over the years, it adds up. Since 1996, when CPI was introduced, its measure of cumulative inflation is 35.6 per cent, while RPI has it at 53.6 per cent. A pensioner who retired that year and whose pension was uplifted by RPI would now be 13 per cent better off than one whose pension was uplifted by CPI.

Some of this difference, which has averaged 0.88 percentage points a year, is due to what is included in the basket of goods and services whose prices are recorded as the first step in constructing the index. But a substantial part of the difference, an average of 0.53 percentage points a year, has been the result of the so-called “formula effect” – the way in which changes in prices are aggregated into an index.

This gap, says Dr Mark Courtney in a critique published this month on the Social Science Research Network, is “embarrassingly large for a mere difference in statistical technique, and much larger than in other countries”. In 2010 it widened to an average of 0.81 percentage points, which the Office for National Statistics attributed to changes in the way it collected prices for clothing and footwear.

In constructing both indices, the first stage involves working out the price growth (or decline) for each of the 680-odd items included in the basket. The RPI does this by averaging the changes between the present period and the previous one for each set of prices collected by its monitors, using the arithmetic mean. The CPI, in contrast, calculates from much the same data the geometric mean of the price changes. (For n items, the arithmetic mean is the sum of the values divided by n; the geometric mean results from multiplying all values together and taking the nth root.)

It can be shown mathematically that the wider the range of price changes for any item in any period, the greater the difference between the geometric and arithmetic means. The widening gap between CPI and RPI is the result, says the ONS, of changes to the way it measured prices – allowing sales goods to be included in the base period, for example, or including all items in the base period even if they were likely to go out of stock. That increased the dispersion of price changes, and hence the gap between CPI and RPI.

But Dr Courtney argues that, while true, this misses the real issue, which is what determines these prices in the first place. The indices assume that price increases are the result of changes on the supply side: higher wages for workers producing the goods, higher raw material prices, higher energy or transport costs, etc. They ignore changes on the demand side, such as changes in fashion that may drive down the price of last year’s clothes and enable retailers to charge a premium on this year’s more fashionable items. Such changes, he argues, lead to underestimates of the inflation rate because the ways the index is constructed gives greater weight to price falls than to price rises.   

The second problem he identifies is that the UK uses price data originally devised for the RPI to construct the CPI. Other countries have much more tightly defined categories of items for which prices are collected: either more homogenous categories, or those that have high levels of substitutability. This makes them appropriate for an index constructed using the geometric mean, which assumes that consumers will switch from one product to another when prices change.

But RPI was designed differently, with looser categories and a different method of averaging which were not ideal for the CPI. This didn’t matter much while the CPI were simply used as a harmonised measure of inflation within the EU, its original purpose. The CPI may have underestimated UK inflation, but it did so in a consistent way, so could be used to set a target, so long as that target was lower than it was for RPI (a fact recognised by lowering the target from 2.5 per cent to 2.0 per cent). But when CPI was adopted for benefit and pension uprating, its defects as an inflation measure become very important indeed. 

A second attack on CPI has come from Dr Gareth Jones, in a letter to Sir Michael Scholar, chair of the UK Statistics Authority. He argues that the use of the geometric mean does not represent how consumers actually behave. What the geometric mean actually assumes is that brands that gain sales will be those whose percentage increases in price are below average, regardless of their actual price, he maintains. And that is implausible.

Suppose we have two brands priced initially at £1 and 50p. If the more expensive brand increases in price by 2 per cent and the cheaper brand by 10 per cent, their prices will be £1.02 and 55p respectively. Will consumers switch to the more expensive brand because the differential in price has fallen from 50p to 47p? He argues they won’t.

But replying on behalf of Sir Michael, National Statistician Jil Matheson says yes they will, because of the greater utility or product satisfaction provided by the more expensive product. She cites a rival case of two brands costing 60p and 50p. One increases by 5 per cent to 63p, the other by 20 per cent to 60p. The price differential has fallen from 10p to 3p, and consumers will switch to the dearer brand because they now perceive it to be better value.

The difference between these two examples, of course, is homogeneity. Dr Jones has chosen brands that differ greatly in price, Dr Matheson brands whose prices are close. Both make a plausible case, based on their premises.

But which represents reality better? In the clothing market, where price differentials are large and where the ONS tripped up, one might feel that Dr Jones’ example is closer to real life. That brings us back to Dr Courtney’s call for more tightly-drawn and homogenous item categories to lower the dispersion of relative price changes, and the use where appropriate of a different averaging method in the first stage of calculation. .

The RSS has called for a re-examination of this stage, using retailers’ knowledge of how consumers behave, coupled with appropriate data collection, and the ONS has undertaken to examine the issue. But what the RSS seeks is a better version of the RPI, with the CPI reverting to its old name, the Harmonised Index of Consumer Prices, so as to remove confusion over what it actually measures.

Would these changes, desirable as they are, induce the Government to revert to RPI for uprating pensions and benefits? Given that it would cost more, that seems very unlikely. The public will continue to pay for the confusion that enabled a cash-strapped government to take cover behind an index that is not fit for purpose.

Update, August 25:

Dr Jones himself is unconvinced by Jil Matheson’s reply. He says that in her example you could replace 60p by £60 and the degree of substitution would be unchanged. Claims that the notion that price levels of different brands do not affect substitution behaviour is “really beyond reasonable belief”, he says, consumers often being unaware of recent prices changes, and basing their decisions on price levels.

Countries that have used the geometric mean (GM) in their price indices have made “a serious error” to which users of ONS data, including the media, should be alerted. He adds that there are 9 EU countries, including Germany, that do not use it.  “It is therefore quite wrong to say that the UK is in any way following an international consensus”.

Dr Jones has put these views in a response to UKSA, which will no doubt appear on UKSA’s website soon.