The Chancellor of the Exchequer is not getting away unchallenged with his decision to link benefits and pensions to a different inflation measure, mentioned earlier on these pages. 
 
George Osborne has announced that in future the index used will be the Consumer Price Index (CPI), not the Retail Price Index (RPI). He’s given private pension schemes the right to opt for the change, too, so long as the rules of the scheme do not specifically refer to RPI.
 
The advantage to those responsible for paying pensions and benefits is that CPI rises more slowly than RPI – so they’ll save money. That’s probably enough of an argument to satisfy Mr Osborne. But those in receipt of benefits and pensions will lose: and over a lifetime, they’ll lose a lot.
 
Is it satisfactory for this change to be made without consultation or argument? And why, if the indices differ, should one be chosen over another? Professor David Hand, President of the Royal Statistical Society, has just written a letter to Sir Michael Scholar, chair of the UK Statistics Authority, raising a series of questions along these lines. 
 
First, he asks why the CPI is now the headline index even though it is not nesessarily the best for all purposes. It excludes housing costs for owner-occupiers (such as insurance), council tax, vehicle excise duty, and TV licences, all costs that consumers have to bear. Its use as the principal index means that, for example, trade unions arguing for pay rises have to justify it against an index that does not reflect all the extra costs their members may be paying.
 
But it includes foreign students university tuition fees and foreign exchange commission for tourists changing their own currency into sterling, which for most UK citizens are irrelevant.
 
“We do not think that CPI should have sole star billing” Professor Hand argues. Other EU countries, including France, Germany, Italy, Spain and the Netherlands, he says, all publish their own national inflation indices alongside CPI, which was originally developed by the EU as the Harmonised Index for Consumer Prices to make international comparisons possible. “Giving prominence to CPI ahead of other indices means that users are implictly being encouraged to use it for purposes, such as wage negotiations, for which it is not ideal.”
 
Why do RPI and CPI differ? Partly because they count slightly different things, but also because they use a different method of calculation – the so-called Formula Effect. Even if they counted identical things, they would still differ by a substantial amount. Over the past five years, the difference in annual inflation rates due to the Formula Effect has never been less than 0.43 per cent, and has been as high recently as 0.86 per cent.
 
RPI uses the arithmetic mean of prices rises for goods and services, weighted to reflect the consumption pattern of UK households. CPI uses the geometric mean which, ONS argues, allows for the substitution of cheaper goods for more expensive ones when relative prices change. (For an explanation of the difference, try this link to a paper prepared by the special adviser to a Lord selct committee investigating the Monetary Policy Committee of the Bank of England.) 
 
There is a further subtlety. In RPI, the arithmetic mean can be calculated either by the “ratio of averages” or the “average of relatives” method. Let us assume an index based on prices of 30 different goods. The relatives are the changes in prices for each good over one year. How do you work out the index?
 
You can tot up the prices for all 30 goods in year one, and divide by 30 to get an average price. Do the same for the second year, then take the ratio betwen the two averages: the ratio of averages. Or you can calculate relatives (price changes) for each of the 30 goods between year 1 and year 2 and average the relatives. The first result is a ratio of two averages: the second an average of 30 relatives.
 
Just to keep it simple, RPI uses both: ratio of averages for homogenous items, and average of relatives for items with a wide distribution of price levels. According to Professor Hand. the UK uses average of relatives to a greater extent than other countries, and this may help explain why there is such a big difference between CPI and RPI. But nobody seems to know.
 
“We consider it highly unsatisfactory that a difference in statistical treatment should generate such a substantial difference in the two indices” he says. “We are not aware of any other country where the difference is as great.”
 
The result may be that RPI overstates inflation. If it does, it means that holders of index-linked gilts are being overcompensated for inflation at the cost of the taxpayer. Even if not, it would be nice to have a proper explanation of how these differences arise, and why one index should be preferred to another, beyond the convenience of saving the Treasury money.
 
Finally Professor Hand calls for greater openeness in the work of the Consumer Prices Advisory Committee, recently established – including the publication of summary minutes, and some idea of its work programme.
 
“The Chancellor’s decision makes matters more urgent and increases the need for a more comprehensive review” he concludes. “The political and legal factors involved make this all the more necessary.”