Today the September 2010 inflation numbers were published by the Office for National Statistics. The September inflation figures are particularly important because they are typically used for the annual inflation adjustments to many taxes, benefits and tax credits.

In the June Budget, the Chancellor announced that benefits, tax credits and public service pensions would be uprated with the Consumer Prices Index (CPI) rather than the Retail Prices Index (RPI) (which has been used to uprate universal benefits) or Rossi Index (which has been used to uprate means-tested benefits) from April 2011 (more generous increases are to apply to the Basic State Pension and the Pension Credit). This September, CPI inflation was 3.1% , the RPI inflation was 4.6%, and Rossi inflation was 4.8%.

The CPI tends to give a lower measure of inflation than both the RPI and Rossi indices. This change in indexation rules is forecast to save the government £5.8 billion in 2014-15 and increasing amounts thereafter. This was likely an important motive for the change, but the government has also claimed that the CPI provided a better measure of benefit recipients' "inflation experience".

In late August we published an evaluation of this claim. Today we publish an improved version of this analysis, in which we consider alternative assumptions, use the data more effectively and consider announced future changes to the benefit system rather than just looking at the benefit system as it currently stands. The full list of changes between this new version and our original report can be found in Appendix E of our report.

In comparing these indices there are two key considerations. First, when the prices of goods and services change, households can partially avoid price rises by substituting away from goods that have become relatively more expensive and towards goods that have become relatively cheaper. As we previously observed, the way the CPI is calculated is designed to attempt to take some account of this (given certain assumptions about the way consumers behave) whereas the RPI and Rossi indices are not. In this respect, the CPI is a superior measure. The ONS reports that this is the most important reason for the difference between the CPI and the RPI.

Second, the CPI also differs from the other indices in terms of the goods and services it includes. Most importantly, compared to the RPI, the CPI excludes mortgage interest and Council Tax costs, and compared to Rossi, which already excludes these items, the CPI includes rents.

Do the differences in the coverage of the CPI make it a better measure of inflation for benefit recipients than the current combination of the RPI and Rossi? To assess this we use household survey data to look at the proportion of recipient households who could be considered insulated from changes in both mortgage interest and Council Tax costs. In this exercise, we only look at working age households, as pensions are subject to different indexation rules.

At present, it appears that the vast majority of those on RPI-linked benefits are not insulated from mortgage interest and council tax changes. This group is largely made up of households receiving only Child Benefit, some of whom might be affluent households.

Those on means-tested benefits that have hitherto been indexed to the Rossi are largely insulated from changes in mortgage interest and Council Tax, but as both Rossi and the CPI exclude these costs, this does not favour one or the other. At present the exclusion of rents from Rossi - an item included in the CPI - does favour the Rossi, as the vast majority of those receiving Rossi-linked benefits appear insulated from rental costs (in most cases because they receive Housing Benefit).This means that under current benefit rules the coverage of the CPI does not look like an improvement over the status quo.

However, changes to the benefit system announced in the Budget, or since, alter this assessment going forward. From April 2013, for instance, Housing Benefit for those renting in the private sector (Local Housing Allowance) will no longer be linked to local rents but will instead be uprated using the CPI. This means that fewer households receiving means-tested benefits will be insulated from changes in rental costs than before (this is something we consider in our revised analysis). A cap on total benefit payments linked to average family earnings announced recently might have a similar effect. These changes may make the inclusion of rental costs in the index used to uprate means-tested benefits more appropriate, and so, given these changes, the case for the Rossi over the CPI - on a coverage basis - will weaken.

To summarise, the fact that it accounts for consumers' ability to substitute between goods and services favours the CPI. For those on universal benefits, the coverage of goods and services in the RPI is superior to the CPI. For those on means-tested benefits, with whom we may be more concerned, the Rossi's coverage of goods and services is superior to the CPI's given the current benefit system, but the case against the CPI may weaken, once currently announced changes to the system take full effect.

Our analysis here has been concerned solely with the technical question of which index is a better measure of the inflation experience of households receiving benefits. This is, of course, an entirely separate issue from the broader question of how generous one thinks benefits should be.