Working paper No. 2
The long-run difference between
RPI and CPI inflation
Ruth Miller
November 2011© Crown copyright 2011
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The long-run difference between RPI and CPI
inflation
Ruth Miller
Office for Budget Responsibility

Abstract

Between 1989 and 2011 Retail Prices Index (RPI) inflation tended to be around 0.7
percentage points higher than Consumer Prices Index (CPI) inflation on average. Recent
developments suggest that the long-run difference between these measures may besignificantly higher in the future. This paper decomposes the differences in RPI and CPI
inflation and looks at the prospects for the evolution of the wedge between the two
measures over the long term. Possible methodological developments to the CPI and RPI
could have a substantial impact on the difference between RPI and CPI inflation, andconstitute one of the main uncertainties surrounding the long-term difference between
the two measures.

JEL references: E30, E31
Keywords: Inflation, Consumer Prices Index, Retail Prices Index
I am grateful for comments from Philip Gooding, Richard Campbell and Darren Morgan
at the ONS and colleagues at the Office for Budget Responsibility.

Contents

Chapter 1

Introduction......................................................................................... 1

Chapter 2

Decomposing the differences in the RPI and CPI .................................... 5

Chapter 3

Prospects for the long-term wedge between RPI/RPIX and CPI inflation.. 29

Annex A

Coverage of inflation indices .............................................................. 33

Annex BONS methodology for measuring the RPI-CPI wedge ........................... 35

Working paper No. 2: The long-run
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I

1

Introduction

1.1

In assessing the outlook for the economy and the public finances, we areinterested in a number of measures of inflation. The Consumer Prices Index (CPI)and the Retail Prices Index (RPI) are both average measures of the prices of goods
and services, based on the cost of a basket of goods and services. However,
although the basic approach to the measurement of inflation (the rate of changeof the index) using these indices is the same, there are differences which arise
due to their coverage, the way in which they are constructed and therepresentative population covered by the indices. 1 Other measures of inflation
include RPIX, which excludes mortgage interest payments and was the Bank ofEngland’s policy target until it was switched to CPI in 2003.

1.2

The RPI and CPI measures of inflation are important because they have different
effects on the OBR’s fiscal forecast. The Government’s stated policy is to use CPI
for the indexation of benefits, tax credits and public service pensions. The RPI is
used for the uprating of index-linked gilts and the revalorisation of excise duties.
The differences are also important because if the Bank of England’s policy target
for CPI inflation is set at 2 per cent, a permanent increase in the wedge between
the RPI and CPI measures of inflation would suggest that this is equivalent to ahigher corresponding rate of RPI and RPIX inflation than would otherwise havebeen the case.

1.3

Chart 1.1 shows the wedge between the different measures of inflation since1997. On average in 2011, the differential between RPIX and CPI inflation has
been around 0.9 percentage points and 0.8 percentage points between RPI and
CPI inflation. In October 2011, the wedge between RPIX and CPI inflation iscurrently around 0.6 percentage points and around 0.4 percentage points
between RPI and CPI inflation.

1.4

One objective of this paper is to help distinguish between short-term factors
affecting the wedge and longer-term factors. The short-run differences in thewedge can be quite variable. Part of the difference between RPI and CPI relates tothe fact that the RPI includes some components that are not included in the CPI,
such as housing components and mortgage interest payments (MIPs) (Table 2.2).

1

For more details see Office for National Statistics (ONS), July 2011, History of and differences between theConsumer Prices Index and Retail Prices Index.

1

Working paper No. 2: The long-run
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Introduction

As these components fluctuate over the short term so do the differences between
RPI and CPI inflation. One example is the large downward effect that the housing
component and MIPs had on the wedge between RPI/RPIX and CPI inflation in
2009.

Chart 1.1: The wedge between RPI/RPIX and CPI inflation since 1997
3
2

Percentage points

1
0
-1
-2
-3
-4
1997
Source: ONS

1999

2001

2003

2005

RPI-CPI

2007

2009

2011

RPIX-CPI

1.5

For a number of years a widely held view was that the long-run difference
between RPIX and CPI inflation rates was around ¾ percentage points. 2 Indeed,since around 1989, RPI and RPIX inflation have tended to be around 0.7
percentage points higher than CPI inflation, on average.

1.6

However more recent developments suggest that the long-run difference is likely
to be significantly wider in the future. The March 2011 Economic and fiscal
outlook (EFO) stated that the long-run difference is expected to be around 1.2
percentage points between RPI and CPI inflation. This was based on theassumption that recent rises in the ‘formula effect’, one of the components of thewedge between the RPI and CPI, will begin to stabilise and the larger contribution
from the formula effect in 2010 will persist.

1.7

Chapter 2 of this paper looks at the decomposition of the differences between
these measures of inflation and looks at each component of the wedge in turn.

2

Nickell, S. Winter 2003, Two current monetary policy issues, Bank of England Quarterly bulletin.

Working paper No. 2: The long-run
difference between RPI and CPI inflation2

Introduction

Chapter 3 focuses on the long-term prospects for the difference between RPI and
CPI inflation. The paper firstly considers the differences between the RPIX and CPI
measures of inflation and then looks in more detail at MIPs (excluded from the
RPIX inflation measure) to gauge the prospects for the long-run differences
between RPI and CPI inflation.
1.8

Based on the decomposition of the differences between these measures, further
analysis in this paper suggests that a plausible range for the long-run difference
between RPI and CPI inflation is around 1.3 to 1.5 percentage points (Table 3.1).
For the basis of our November 2011 EFO, we assume that the difference
between RPI and CPI inflation is around 1.4 percentage points in the long run.
This represents the mid-point of the plausible range of estimates set out in
Chapter 3.

3Working paper No. 2: The long-run
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Working paper No. 2: The long-run
difference between RPI and CPI inflation4

2

Decomposing the differencesin the RPI and CPI

2.1

There are four main components that account for the difference between RPI and
CPI inflation.


The formula effect, which occurs as a result of the combination of the use of
the geometric mean (GM) and arithmetic mean (AM) to aggregate pricechanges at a basic level in the CPI, whereas the RPI uses the AM only.



The RPI and RPIX include housing components such as owner-occupiers’
housing depreciation and council tax and rates, which are currently
excluded from the CPI. In addition the RPI further includes mortgage interest
payments (MIPs).



Other differences in coverage arise as the CPI includes a number ofcomponents which are not included in the RPI/RPIX such as brokerage fees,
student accommodation fees and overseas student’s tuition fees. The RPI
and RPIX also proxy new car prices and include vehicle excise duty (VED),
trade union subscriptions and TV licence fees, which are not currently
included in the CPI. 1

Other differences include the weights given to the components of eachindex. These arise due to the use of different data sources and population
bases to calculate the weights in the CPI and RPI.

1

As part of the ONS’s annual review of the basket of goods included in the CPI and the RPI in 2012, theONS propose to include TV licence fees, VED and trade union subscriptions in the CPI. These items are
already included in the RPI. Subject to the approval of the UK Statistics Authority, these items will be includedin the CPI in 2012, reducing the coverage differences between the RPI and CPI.

5

Working paper No. 2: The long-run
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Decomposing the differences in the RPI and CPI

Table 2.1: Contributions to the difference in RPIX, RPI and CPI inflation
rates
Current1
Formula effectHousing (ex. MIPs)
Other differences incoverage
Other differences inc.
weights
Total RPIX-CPI wedge3
MIPs
Total RPI-CPI wedge3
1

Average2
Minimum
Maximum(2005-2011) (2005-2011) (2005-2011)

1.0
-0.1
-0.2

0.6
0.3
-0.1

0.4
-0.6
-0.3

1.0
1.0
0.2

Standard
deviation(2005-2011)
0.2
0.4
0.1

-0.3

-0.3

-1.0

0.2

0.3

0.6
0.0
0.4

0.6
0.0
0.5

-0.8
-2.8
-3.5

1.8
1.5
2.3

0.6
1.1
1.5

October 2011
The average, minimum, maximum and standard deviation are calculated from Jan 2005 to October 2011. The ONSchanged the methodology which it uses to calculate the contributions to the wedge, designed to provide a more accurate
breakdown. Data using the revised methodology (presented here) begins in 2005.
3
The components may not sum to the total wedge between RPI/RPIX and CPI inflation, as the total wedge is calculatedusing published RPI, RPIX and CPI inflation rates rounded to 1 decimal place.
2

Chart 2.1: Decomposition of the difference between RPIX and CPI inflation
2.0

Percentage points

1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
1997

1999
Housing

2001

2003

Coverage2005
Formula2007
Weights

2009

2011

RPIX-CPI Rounded*The ONS methodology used to calculate contributions to the wedge between the RPI and CPI inflation changed in 2005. The chart shows
the data using the previous methodology up to 2005 and the revised methodology which is only available from 2005 onwards.
Source: ONS

2.2

Table 2.1 shows the contributions to the difference between the RPIX/RPI and CPI
inflation rates from each of the components. The historical decomposition of thedifference in RPIX and CPI inflation is also shown in Chart 2.1. This shows that
there are large fluctuations in the wedge due to the movements in housing
components, such as the downward effect that the housing component had on
the wedge in 2009. The contribution from the formula effect on the other hand

Working paper No. 2: The long-run
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6

Decomposing the differences in the RPI and CPI

has been relatively stable over the past but has increased significantly since
2010.
2.3

The data in Table 2.1 are based on the Office for National Statistics (ONS)’srevised methodology for calculating contributions to the wedge, which begins in2005. The revised methodology is a ‘contributions’ approach which gives anestimate of the effect of a particular component on the annual rate of CPI or RPI
inflation. By comparison, the previous methodology ran from 1997 to 2005 andwas calculated by using annual changes and adding/subtracting them from theheadline rates to calculate each component. 2 Therefore contributions before andafter 2005 are based on two different methodologies and so cannot be easily
compared. Annex B looks at the comparison between the two methodologies inmore detail and the decomposition since 1997.

The ‘formula effect’
2.4

The ‘formula effect’ occurs as a result of the use of a combination of thegeometric mean (GM) and arithmetic mean (AM) to aggregate prices at the basic
level in the CPI, whereas the RPI uses the AM only. The former is better-suited toaccounting for the effective of substitution between goods and services whenrelative prices change. The GM of a given set of non-identical positive numbers islower than the AM of the same set of numbers. Before 2010, the formula effectgenerally accounted for approximately 0.5 percentage points of the long-run
difference between RPI/RPIX and CPI inflation.

2.5

However the difference between the RPI and CPI inflation rates as a result ofusing different formulae has risen from around 0.5 percentage points over 2009
to an average of around 0.8 percentage points over 2010. The ONS has
indicated that changes in the way in which prices of clothing are collected, first
implemented from January 2010, have the potential to increase the formulaeffect 3 (Chart 2.2, Chart 2.3). The extent that the results using a GM or AM differ
depends on the dispersion of the ratios of the prices that are collected in thecurrent period with the matching prices collected in the base period. The changes
to the collection practices for clothing prices have the potential to increase thedispersion of these price ratios.

2.6

At the beginning of 2011, the formula effect has increased yet further, remaining
at around 1 percentage point from February to October 2011. The largest

2

See ONS Information Note, Consumer Prices Index and Retail Prices Index – analysing differences.

3

More information can be found in the ONS information note, January 2011, CPI and RPI: the increased
impact of the formula effect in 2010.

7

Working paper No. 2: The long-run
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Decomposing the differences in the RPI and CPI

contribution from the formula effect to the wedge since 1997 occurred in March
this year.

Chart 2.2: Contribution of each division to the formula effectMiscellaneous goods & services

1.2

Restaurants & hotels

1.0

Education

Percentage points

0.8

Recreation & culture
Communication

0.6

Transport
0.4

HealthFurniture, household equipment& maintenance
Housing,water,electricity,gas &other fuels
Clothing & footwear

0.2
0.0

Alcoholic beverages-0.2
Sep-11

Jul-11

May-11Mar-11

Jan-11

Nov-10

Sep-10Jul-10May-10Mar-10Jan-10

Nov-09Sep-09Jul-09

May-09Mar-09

Jan-09

Food & non-alcoholic beverages
All

Source: ONS

Chart 2.3: Clothing and footwear prices in RPI and CPI
15

Per cent change

10
5
0
-5
-10
-15
1997

Source: ONS

1999

2001

2003

2005

2007

Difference
RPI clothing and footwear annual rate
CPI clothing and footwear annual rate

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8

2009

2011

Decomposing the differences in the RPI and CPI

2.7

The OBR previously assumed that the formula effect would contribute around 0.5
percentage points to the long run wedge between RPI and CPI inflation,
consistent with the average contribution from the formula effect over the past. The
OBR’s March 2011 forecast was based on the assumption that the recent rises in
the formula effect since 2010 will begin to stabilise and that the larger
contribution from the formula effect in 2010 will persist. In the March 2011
Economic and fiscal outlook (EFO), we assumed that there would be a permanent
increase in the difference between RPI and CPI inflation of around 0.3
percentage points (i.e. the formula effect is expected to contribute around 0.8
percentage points to the long-term wedge between RPI and CPI inflation).

2.8

However, the average contribution from the formula effect from the beginning of2010 to October 2011 is currently slightly higher at around 0.9 percentage
points. By April 2011, the improvements to the collection practices for clothes
prices had been in place for a year, so the annual price rates were no longer
affected by methodological changes. Since April, we have not seen any
significant falls in the contribution from clothing and footwear to the formulaeffect. One possibility is the formula effect could continue to contribute a larger
amount to the wedge between RPI and CPI inflation in the long run. Chart 2.2
shows that there has also been a small increase in the contribution from therecreation and culture component to the formula effect. This has also been
contributing to the recent increases in the contribution from the formula effect tothe wedge between RPI and CPI inflation over 2011. Future inflation data willcontinue to be important in indicating the persistence of the recent increases in
the formula effect.

2.9

A further uncertainty is that the ONS are currently undertaking a review of themethods used to measure clothing prices in the CPI and RPI. This will look at why
current methods might be contributing to the difference that currently exists
between CPI and RPI measures of clothing inflation and aims to develop
alternative compilation methods. More broadly, the ONS is currently looking at
the degree to which consumers substitute between goods when their relative
prices change i.e. the elasticity of substitution for each product in the CPI and
RPI. 4 Where a product has a larger elasticity of substitution a GM is more suitable
than an AM given that it captures the effects of the substitution between goods. By
July 2012, the ONS aims to use elasticity of substitution estimates to inform thechoice of formula that is used to aggregate prices.

4

For more details see National Statistician’s Consumer Prices Advisory Committee, September 2011,
Estimating Price Elasticities and National Statistician’s Consumer Prices Advisory Committee, July 2011,
Measurement of Clothing Prices.

9

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Decomposing the differences in the RPI and CPI

2.10

In the event that this work leads to changes in current practices for the collectionof clothes prices, this may have some impact on the recent increase in the wedgethat we have seen. It will therefore be important to keep up to date with any
further developments from the ONS.

2.11

Based on the data that are currently available (i.e. notwithstanding the outcomeof the ONS review of methods used to measure clothing inflation), thecontribution from the long-term formula effect could be higher than 0.8
percentage points and fall somewhere in the region of 0.8 percentage points to 1
percentage point.

Housing components
2.12

The RPI includes housing components comprised of: owner-occupiers’ housing
depreciation, council tax and rates, rent, water and other charges, repairs andmaintenance charges, do-it-yourself materials, dwelling insurance and groundrent and mortgage interest payments (MIPs). In contrast the RPIX excludes MIPs.
The CPI excludes MIPs, owner-occupied housing costs and council tax, but
includes rent, minor repairs and maintenance costs, water and other charges(Table 2.2).

Table 2.2: Housing coverage of RPI, RPIX and CPI
Mortgage interest payments (MIPs)
House depreciation
Council tax
Rents
Building insurance and ground rentHouse transaction costs e.g. estate agents’ fees,
surveyors costs and conveyancing fees

RPI
√
√
√
√
√
√

RPIX

CPI

√
√
√
√
√

√

a) Housing coverage in the RPIX
2.13

5

The most significant differences in housing components between the RPIX and CPI
come from housing depreciation and council tax. 5 The contribution from housing
depends on developments in the housing market, which has exhibited
considerable volatility in the past, for instance in 2009, and can have a large
impact on the wedge between RPI and CPI inflation (Chart 2.4).

These components have a total weight of 9.4 per cent in the RPI in 2011.

Working paper No. 2: The long-run
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Decomposing the differences in the RPI and CPI

2.14

A smoothed version of the Department for Communities and Local Government(DCLG) house price index is used as a proxy for the housing depreciation
component in the RPI/RPIX. Chart 2.4 shows how the housing contribution(excluding MIPs) to the wedge between RPI and CPI inflation has moved broadly
in line with house price growth. 6

1.2

15
House price growth on year earlier

1.0
10

0.8
0.6

5

0.4
0.2

0

0.0
-5

Housing contribution to RPIX-CPI wedge (percentage
points)Chart 2.4: Contribution of housing components to the wedge between RPI
and CPI inflation

-0.2
-0.4

-10

-0.6
-15
2005

-0.8
2006

2007

2008

2009

2010

2011

DCLG mix-adjusted average house price (LHS)
Housing excl. MIPs contribution to RPIX-CPI wedge (RHS)
Source: DCLG, ONS

2.15

In the medium term, we assume that house prices will grow at a similar rate to
the trend growth in average earnings of around 4.7 per cent. In addition, there
has been a general upward trend in the weight in the RPI of the housing
depreciation component from 3 per cent in 1995 to 5.4 per cent in 2011.

2.16

To calculate the contribution each component makes to the wedge between RPI
and CPI inflation, the ONS takes the difference between the contribution acomponent makes to CPI inflation from its respective contribution to RPI inflation.
For instance, in June 2010, MIPs contributed 0.15 percentage points to RPI
inflation. As MIPs are excluded from the CPI, it makes no contribution to the CPI
index, so the difference between RPI and CPI inflation rates as a result of MIPs is

6

The housing depreciation component of the RPI does not follow DCLG house price index exactly as the RPI
excludes the households in the top 4 per cent income bracket. In addition, the DCLG house price index is
not available until a month after it is needed so it is used on a smoothed and lagged basis.

11

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Decomposing the differences in the RPI and CPI

0.15 percentage points. 7 Based on the weight of 5.4 per cent in 2011 for the
housing depreciation component, this suggests that the long-term contribution to
the wedge would be around 0.25 percentage points 8 (i.e. assuming house prices
will grow at a similar rate to growth in average earnings of around 4.7 per centmultiplied by 5.4 per cent). 9
2.17

The CPI also excludes council tax as it is treated as a direct tax in the National
Accounts. It has therefore not been considered as household consumption and is
excluded from the CPI, which is based on Household Final Monetary
Consumption in the National Accounts. 10 However, the decision as to whether toinclude council tax in the CPI is currently being considered further by theConsumer Prices Advisory Committee (CPAC) alongside the work by the ONS on
the inclusion of owner occupiers’ housing costs. 11

2.18

Over the long run we might assume that a plausible assumption for the growth ofcouncil tax is around 3 per cent based on average growth rates over recent
years. Based on the weight of 4 per cent in 2011 for the council tax component,
this suggests that the long-term contribution to the wedge would be around 0.1
percentage points.

2.19

A plausible assumption for the combined contribution to the wedge from housing
components in the RPIX, such as housing depreciation and council tax is around0.35 percentage points.

b) Mortgage interest payments (MIPs)
2.20

The RPI includes MIPs, which are excluded from the CPI and RPIX. Although thecontribution to the wedge from MIPs averages at zero over time (see Table 2.1),

7

For more details on the ONS methodology for explaining the differences between the CPI and RPI see
ONS Information note, Consumer Prices Index and Retail Prices Index – analysing differences.
8

The ONS are currently developing owner occupiers’ housing costs (OOH) indices for the potential
inclusion in the CPI. This calculation assumes that there are no adjustments to the CPI to include owneroccupied housing costs. For more details on OOH see the section on Risks and uncertainties.
9

It is also possible to calculate the contribution that the housing depreciation component makes to thewedge between RPI and CPI inflation by taking the difference between the assumed long-run rate forhousing depreciation (i.e. around 4.7 per cent) and annual CPI inflation in the long run, of 2 per cent.
Taking this average annual rate and the weight of housing depreciation in the RPI also gives a contribution
to the wedge. We do not use this approach as we try to be as consistent with the ONS methodology as
possible.
10

For more details see ONS, July 2011, History of and differences between the Consumer Prices Index andRetail Prices Index.

11

For more details see National Statistician’s Consumer Prices Advisory Committee, September 2011, Item
Coverage in the Consumer Prices Index.

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Decomposing the differences in the RPI and CPI

this is the main source of volatility in the wedge between RPI and CPI inflation.
Chart 2.5 shows the contribution to the difference between RPI and CPI inflationfrom the MIPs component.

Chart 2.5: Contribution of MIPs to the difference between RPI and CPI
inflation
3
2

Percentage points

1
0
-1
-2
-3
-4
2005
Source: ONS

2006

2007

2008

2009

MIPs contribution to RPI-CPI wedge

2010

2011

RPI-CPI

2.21

To model the MIPs component, the ONS calculates the average debt outstanding
on 276 different vintages of mortgages and this is revalued based on movements
in house prices. 12 This average debt tends to rise over time, given that the
average mortgage payment in the latest month is generally much higher than the
one dropping out. Thus, there will be an upward drift in the MIPs index, even withno changes in mortgage rates.

2.22

Over the long term we might expect mortgage interest payments to grow in linewith the average earnings growth assumption and we assume interest rates areunchanged. 13 As MIPs have a weight of 3.2 per cent in the RPI in 2011, thiswould imply the long-term contribution of MIPs to the wedge between RPI and
CPI inflation is around 0.15 percentage points.

12 So, each month the average debt will change, as the value of the latest vintage will tend to reflect latest

house prices, while the oldest vintage drops out; hence the average debt tends to change with changes inhouse prices.
13

As MIPs are not necessarily rising in line with the average earnings growth assumption by the end of ourforecast, RPI does not always return to the long-term rate in 5 years time in our forecast.

13

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Other differences in coverage and differences inweights
Other differences in coverage
2.23

Other differences in coverage arise as the CPI includes brokerage fees, student
accommodation fees and overseas student’s tuition fees. The RPIX includes VED,
trade union subscriptions, TV licence fees and proxies new car prices (Table 2.3).

Table 2.3: Other differences in coverage of RPI, RPIX and CPI
RPI
√
√
√

Trade union subscriptions
Vehicle excise duty (VED)TV licence fees
Unit trust and stockbroker fees
University accommodation fees
Foreign students’ university tuition fees
New car prices

RPIX
√
√
√

CPI

√
√
√
√

2.24

Other differences in coverage are currently contributing around -0.2 percentage
points compared to their average contribution to the wedge over the past 6
years 14 of around -0.1 percentage points (Table 2.1). Over the longer run, since1997, the average contribution from other differences in coverage has also beenaround -0.1 percentage points. However the average since 1997 uses a mixtureof the ONS’s previous and revised methodologies to calculate the breakdown in
the wedge between RPI and CPI inflation (Table B.3 in Annex B).

2.25

Previously, a large contribution to the coverage component has come from themeasurement of car prices. Aside from car prices, we do not have the relevant
historical time series for the item level data available from the ONS for the othercoverage differences shown in Table 2.3. However, these generally tend to havesmaller weights in the RPI/CPI than those for car prices. Unless the average pricechanges for these components are significantly stronger or weaker than the othercomponents, we might therefore assume that they do not contribute as much to
the wedge as the effect from car prices.

2.26

As part of the ONS’s annual review of the basket of goods included in the CPI
and the RPI in 2012, the ONS propose to include TV licence fees, VED and tradeunion subscriptions in the CPI. These items are already included in the RPI.

14
The average is calculated over the last 6 years as this is the time period over which the revised method isused to construct these series by the ONS.

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Decomposing the differences in the RPI and CPI

Subject to the approval of the UK Statistics Authority, these items will be includedin the CPI in 2012, reducing the coverage differences between the RPI and CPI. 15
2.27

The differences in the measurement of car prices arise as the RPI uses movementsin the prices of used cars as a proxy for new cars. However, as the regulations for
CPI do not permit the use of imputed prices, the CPI uses a specific index for newcars (based on their ‘list’ prices). 16 One disadvantage associated with including
list prices is that it is not necessarily the price paid by consumers as discounts are
not taken into account.

2.28

From around 2002, prices of motor vehicle purchases in the CPI have tended torise faster than prices of vehicle purchases in the RPI (Chart 2.6). Chart 2.7 showsthat there has been a divergence between the annual rate for new cars, based onlist prices and second hand cars in the CPI. The category of purchase of vehicles
has therefore tended to make less of a contribution to RPIX inflation than CPI
inflation, all else equal, reducing the wedge between the two measures ofinflation. Based on the difference in contributions in each month of the purchaseof motor vehicles category to RPI and CPI inflation, the average difference in thecontributions made is around 0.1 percentage points higher in the CPI since1997. 17

2.29

In contrast to this, vehicle prices in the RPI increased sharply during late 2009and early 2010, rising at almost double the annual rate of their equivalent in the
CPI at the beginning of 2010 (Chart 2.6). At its peak in 2010, this added 0.4
percentage points to the wedge between RPI and CPI inflation and around 0.1
percentage points on average in 2010.

2.30

It is possible that these recent effects in 2009 and 2010 will be temporary.
However if the divergence between purchases of vehicle prices from 2002 were
to continue, this could contribute around -0.1 percentage points to the long-run
wedge between RPI and CPI inflation. The average difference in contributions
from this component to RPI and CPI inflation since 1997, as well as from 1997 to
2008, is around -0.1 percentage points. However it seems likely that the inflation
rates for the two series will re-converge to something approaching their previous
degree of correlation, as used car prices cannot fall indefinitely and we might
therefore expect the two series to move together over time.

15

For more details see National Statistician’s Consumer Prices Advisory Committee, September 2011, Item
Coverage in the Consumer Prices Index.

16

This is based on the list prices of a sample of cars covering a range of manufacturers, quality adjusted forchanges in specification. A trade guide is used to obtain the list price, the specification of the model and thecost of any changes in specification.

17

This is also the case for the average difference in contributions up to 2008.

15

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Decomposing the differences in the RPI and CPI

Chart 2.6: Purchase of vehicles in the RPI and CPI
20
15

Annual rate

10
5
0
-5
-10
-15
1997

1999

2001

2003

2005

RPI: Purchase of motor vehicles

2007

2009

2011

CPI: Purchase of vehicles

Source: ONS

Chart 2.7: Annual rate of new and second hand cars in the CPI
20
15

Annual rate

10
5
0

-5

-10
-15
-20
1997
Source: ONS

1999

2001

2003

2005

New carsWorking paper No. 2: The long-run
difference between RPI and CPI inflation

2007

Second hand cars

16

2009

2011

Decomposing the differences in the RPI and CPI

2.31

As part of the development of CPI, the CPAC has recommended to the UK
Statistics Authority that a single measure of new car prices for both the CPI and
RPI should be used. 18 The updated methodology for collecting car prices in the
RPI will reflect new cars rather than using a proxy based on used cars. In
addition, there are planned changes for the measurement of new cars in both the
RPI and CPI to make them more representative of actual transaction prices paid
rather than basing it on ‘list’ prices (i.e. using prices on manufacturer’s websitesthat take into account price discounts).

2.32

These changes are subject to the usual procedure for introducing changes into
the RPI, so the Bank of England will be consulted. A public consultation is also
taking place on these proposals. If agreed the changes are currently scheduled to
be introduced in February 2012 and would eliminate any differences in coverage
as a result of the treatment of new car prices in the RPI and CPI.

Differences in weights
2.33

There are differences in the weights of items in the CPI and the weights of thesame items in the RPI. This is because item weights are derived from different
data sources and population bases (Table 2.4). The CPI weights are largely
calculated from Household Final Monetary Consumption (HFMCE) data takenfrom the National Accounts. By contrast, the RPI relies on data from the Living
Costs and Food survey and relates to the expenditure of households only,
excluding the highest income households and pensioner households which aremainly dependant on state benefits. 19

Table 2.4: Population coverage of RPI, RPIX and CPI
RPIHighest earning households (top 4 per cent of households byincome)Institutional households
Pensioner households with ¾ of their income coming fromstate pensions and benefits
Spending by foreign visitors to the UK
Spending by UK households abroad

RPIX

CPI
√
√
√
√

√

√

18

For more details see National Statistician’s Consumer Prices Advisory Committee, September 2011,
Improving the Measurement of Car Prices in the CPI and RPI.
19

For more details see ONS, July 2011, History of and differences between the Consumer Prices Index andRetail Prices Index.

17

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Decomposing the differences in the RPI and CPI

2.34

Differences in weights contributed around -0.3 in October 2011 to the wedge
between RPI and CPI inflation. The average contribution to the wedge over the
past 6 years 20 is also around -0.3 percentage points (Table 2.1). There arelimitations associated with observing the long term trend from ONS data forcontributions to the wedge as the data is only available for the past 6 years
based on consistent methodology. The data since 2005 are not necessarily
comparable with the data from 1997 which were based on the previous
methodology for calculating contributions to the wedge (Annex B). In addition, it
is difficult to replicate the calculations by the ONS to measure this component as
it has tended to be calculated as the residual of the other components of thewedge between RPI and CPI inflation, acting to balance the total difference.

2.35

A bottom-up approach discussed here, which approximately decomposes thedifferences in weights by component, although not exact and subject touncertainties, acts as a check on our long-term assumptions. Chart 2.8 shows anapproximate calculation of the contributions to the wedge, by component, due todifferences in weights. It uses the CPI weights in 2011 for the CPI divisions
comparing them with weights of RPI items which have been grouped into thesedivisions. The differences in weights are then used to calculate the contributions
to the wedge between RPI and CPI inflation. 21 For simplicity, long-term
contributions to the wedge are calculated using average annual rates for eachindividual component in the CPI. With the exception of clothing (which is
discussed in more detail below), the average annual rate since 1997 is used foreach component in the CPI. 22 The components which are the main drivers of thecontribution to the wedge as a result of differences in weights are discussed
below.

20

The average is calculated over the last 6 years as this is the time period over which the most recent
method is used to construct these series by the ONS.

21

Although there are uncertainties over the evolution of the weights in the RPI and CPI over the long run, forthese purposes the weights of RPI and CPI items in 2011 are used.
22

This is consistent to the way in which we calculate contributions from the housing components i.e. using
an average annual rate for each component since 1997 rather than taking the difference between the
average annual rate since 1997 and the average annual rate for the CPI of 2 per cent in the long run. We
use this method so that we follow as closely as possible the way in which the ONS calculates contributions to
the differences in RPI and CPI inflation.

Working paper No. 2: The long-run
difference between RPI and CPI inflation18

Decomposing the differences in the RPI and CPI

Chart 2.8: Approximate contributions to differences in weights bycomponent
0.20
0.15

Percentage points

0.10
0.05
0.00
-0.05
-0.10

Education

Recreation &cultureCommunication

Transport

HealthFood & nonalcoholic
beverages
Alcoholicbeverages &tobaccoClothing &footwear
Housing, water,electricity, gas& other Fuels
Furniture,
householdequipment &-0.20

Restaurants &hotelsMiscellaneous
goods &
services
Total
Contribution-0.15

Source: OBR calculationsi) Recreation and culture
2.36

2.37

Based on the average annual rates of each series included in the recreation andculture category since 1997 and the differences in weights in the RPI and CPI in
2011, this division tends to be the most significant positive contributor to thewedge, adding 0.16 percentage points to the difference between RPI and CPI
inflation. The main drivers in this category are:

games, toys and hobbies;

photographic, cinematographic and optical equipment; anddata processing and equipment.

In particular, the weights for each of these items tend to be higher in the CPI thanin the RPI, which is particularly the case for games, toys and hobbies. On
average since 1997, the prices of these items have tended to fall by around 3, 13
and 20 per cent respectively (Chart 2.9). This has tended to increase the wedge
between RPI and CPI inflation by around 0.05 to 0.06 percentage points for eachof these three components.

19

Working paper No. 2: The long-run
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Decomposing the differences in the RPI and CPI

Chart 2.9: Annual rates for items in the recreation and culture division of
CPI
10
5
0

Annual rate

-5
-10
-15
-20
-25
-30
-35
-40
-45
1997

Source: ONS

1999

2001

2003

2005

2007

2009

2011

Games, toys and hobbies
Photographic, cinematographic and optical equipment
Data processing and equipmentii) Transport
2.38

On the basis of the approach set out above, the transport division of the priceindices negatively contributes to the wedge between RPI and CPI inflation due todifferences in weights, by around -0.15 percentage points (Chart 2.8). The
category for transport includes purchase of vehicles (such as second hand car
and new car prices), operation of personal transport equipment (such as fuels
and lubricant prices) and transport services (such as road, railway, sea and air
fares). These are discussed in more detail below.

2.39

Chart 2.10 shows that the airfares index has exhibited a great deal of volatility
and there is often a high level of inflation. Given there are differences in theweights in the RPI and CPI for this category, the level of inflation means that it
can make a non-negligible contribution to the wedge between RPI and CPI
inflation. It is likely that this component will continue to add volatility to the size of
the wedge.

2.40

Given the volatility in the series there is uncertainty in which direction thiscomponent is likely to contribute to the wedge going forwards. Over the period
since 1997, airfares have been growing at an annual rate of around 3.5 per centon average. Due to the differences in weights, this would contribute a reductionof 0.02 percentage points to the wedge between RPI and CPI inflation.

Working paper No. 2: The long-run
difference between RPI and CPI inflation20

Decomposing the differences in the RPI and CPI

2.41

There is a similar story for sea and inland waterway transport, where the annual
rate has exhibited a good deal of volatility (Chart 2.10). The higher weight in the
CPI compared to the RPI implies a reduction in the wedge by around 0.01
percentage points based on the average annual rate since 1997.

Chart 2.10: Annual inflation rate of transport by air and sea
40
30

Annual rate

20
10
0
-10
-20
-30
1997
Source: ONS

2.42

1999

2001

2003

2005

Transport by air

2007

2009

2011

Transport by sea

There are also higher weights in the CPI for the other components of transport
services, such as for road transport. Chart 2.11 shows that the annual rates areless volatile for railway and road transport than for air and sea fares. The
average annual rate is around 4 per cent since 1997 for both series. On thebasis of the approach set out above, this contributes around -0.01 and -0.03
percentage points to the wedge from railway and road transport respectively.

21

Working paper No. 2: The long-run
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Decomposing the differences in the RPI and CPI

Chart 2.11: Annual inflation rate of transport by railway and road1098Annual rate

7
6
5
4
3
2
1
0
1997
Source: ONS

1999

2001

2003

2005

Transport by railway

2007

2009

2011

Transport by road

2.43

Another component of the transport division in the CPI is fuels and lubricants(including petrol, diesel and oil). The weight of fuels and lubricants in the CPI in2011 (4.3 per cent) is smaller than in the RPI (4.6 per cent). Although the weights
have converged slightly since 2010 (4.9 per cent in the RPI, 4.1 per cent in theCPI) there still remains a slight difference. Any large increases in the crude oil
price have generated differences in the contribution of fuels and lubricants to thetwo indices. For example, annual fuels and lubricants prices in 2010 compared
to 2009 contributed around 0.14 percentage points more to RPI inflation than
CPI inflation. On average since 1997, annual fuels and lubricants prices in the
CPI have grown by around 6 per cent (Chart 2.12). This does not have a large
impact on the wedge (around 0.02 percentage points) as a result of thedifference in weights. In the absence of shocks to the oil price, we would expect
the contribution to the wedge to be small.

2.44

Other items within the transport category also have significant differences inweights, such as maintenance and repairs and new cars/proxy for new cars
where the weight in the CPI is higher than that in the RPI. As the average annual
rates for these series since 1997 have been positive, this tends to have a negative
impact on the wedge between RPI and CPI inflation. Used cars on the other hand
have a higher weight in the RPI compared to the CPI. However the averageannual rate since 1997 is -2.3 per cent, contributing -0.02 percentage points tothe wedge.

Working paper No. 2: The long-run
difference between RPI and CPI inflation22

Decomposing the differences in the RPI and CPI

Chart 2.12: Annual inflation rate of fuels and lubricants index
30
25
20

Annual rate

15
10
5
0
-5
-10
-15
-20
1997
Source: ONS

1999

2001

2003

2005

2007

2009

2011

Fuels and lubricantsiii) Miscellaneous goods and services
2.45

Miscellaneous goods and services have also contributed around 0.11 percentage
points to the difference between RPI and CPI inflation as a result of differences inweights.

2.46

In the case of financial services, included in the division of miscellaneous goods
and services, the differences in weights are large. The weight on financial services
in the CPI increased significantly in 2002 from 0.1 per cent in the previous year
to 2.2 per cent and new items were added to the basket, which also suggests thisis an area of coverage differences between the RPI and CPI. 23 Any volatility in theseries therefore has implications for the wedge.

2.47

Given that financial service prices in the CPI fell by 1.6 per cent in October 2011
compared to a year earlier, the differences in weights implies that there will be alarger downward effect on the CPI than on the RPI, which all else equal, would
increase the wedge between RPI and CPI inflation. Since 1997, the averageannual rate of financial services inflation is around -1.8 per cent. Taken together
with the differences in weights in the RPI and CPI, this would add around 0.04
percentage points to the wedge between RPI and CPI inflation. However there
were substantial falls in financial service prices in the early 2000s. Since 2003,

23

For instance, unit trust fees and stockbrokers’ fees are not included in the RPI.

23

Working paper No. 2: The long-run
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Decomposing the differences in the RPI and CPI

the annual rate has averaged around 0.8 per cent, which would instead imply anegative contribution to the wedge of around 0.02 percentage points.

Chart 2.13: Annual inflation rate of financial services index
15
10
5Annual rate

0
-5
-10
-15
-20
-25
-30
1997

1999

2001

2003

Financial services

2005
Average since 1997

2007

2009

2011

Average since 2003

Source: ONS

2.48

24

By contrast, the insurance component of the miscellaneous goods and services
category has a lower weight in the CPI compared to the RPI. 24 Transport
insurance, in particular has a higher weight in the RPI than in the CPI and has
been growing at an annual rate of around 8.6 per cent on average since 1997.
This implies an average contribution to the wedge of around 0.14 percentage
points solely from this component. However the average since 1997 may be
pushed upwards slightly as the annual rate has risen sharply since 2009,
compared to the period between 2002 and 2009 where the annual rate wasmore stable. The average annual rate between 1997 and 2009 was around 5.5
per cent which would add around 0.09 percentage points to the wedge between
RPI and CPI inflation (Chart 2.14).

This is because the CPI only includes the service element whereas the RPI counts the full premium paid.

Working paper No. 2: The long-run
difference between RPI and CPI inflation24

Decomposing the differences in the RPI and CPI

Chart 2.14: Annual inflation rate of transport insurance index
40
35
30

Annual rate

25
20
15
10
5
0
-5
1997

Source: ONS

1999

2001

2003

Transport insurance

2005
Average since 1997

2007

2009

2011

Average up to 2009iv) Clothing and footwear
2.49

The weight of clothing is higher in the CPI than in the RPI. Given that the annual
rate of clothes price inflation is negative on average since 1997, this would
suggest a positive contribution to the wedge between RPI and CPI inflation basedon the differences in weights alone. For example, the average annual rate from1997 to the end of 2009 was around -6 per cent which would contribute around0.08 percentage points to the wedge on the basis of the approach describedabove.

2.50

Since the changes to the ONS collection practices for clothing in 2010, theannual rates have tended to rise, averaging around 0.8 per cent from 2010 to
October 2011 (Chart 2.15). Chart 2.16 shows the index for clothing andfootwear in the CPI, which has generally been on a downward trend before
flattening out in 2010 following the changes in methodology. This is one reason
why using the average annual rate since 1997 for the calculation of thecontribution to the wedge as a result of differences in weights may not always
apply.

2.51

To calculate the approximate contribution to the wedge shown in Chart 2.8, theaverage annual rate of 0.8 per cent is used for clothes prices, to reflect the time
period over which the new methodology has been in place. On this basis, it
might be plausible to assume that clothing reduces the wedge between RPI and
25

Working paper No. 2: The long-run
difference between RPI and CPI inflation

Decomposing the differences in the RPI and CPI

CPI inflation by around 0.01 percentage points as a result of difference inweights.
2.52

The ONS is currently undertaking a review of the methods used to measureclothing inflation in the CPI and RPI. This will analyse why current methods might
be contributing to the disparity that currently exists between CPI and RPI measuresof clothing inflation and aims to develop alternative compilation methods. In theevent that this leads to changes in current practices, this could have an impact on
the contribution to the wedge as a result of differences in weights.

Chart 2.15: Annual inflation rate of clothing index
8642Annual rate

0
-2
-4
-6
-8
-10
-12
-14
1997
Source: ONS

1999

2001

Clothing annual rate

2003

2005

Average since 1997

Working paper No. 2: The long-run
difference between RPI and CPI inflation

26

2007

2009

Average since 20102011

Decomposing the differences in the RPI and CPI

Chart 2.16: Clothing and footwear in the CPI (Index=2005)
200
180

Index (2005=100).

160
140
120
100
80
60
1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

Source: ONSv) Summary
2.53

This method suggests an approximate total long-term contribution of around0.08 percentage points to the wedge between RPI and CPI inflation. Howeverusing the average annual rate since 1997 may not always be a sensible
approach. This is the case for the clothing and footwear component, given the
recent changes in the way clothes prices are measured. To calculate theapproximate contribution to the wedge shown in chart 2.8, the average annual
rate of 0.8 per cent over 2010 and 2011 is used for clothes prices, to reflect thetime period over which the new methodology has been in place. We assume thatclothing reduces the wedge between RPI and CPI inflation by around 0.01
percentage points as a result of difference in weights, rather than adding around0.08 percentage points to the wedge, as would have been the case using the
average annual rate from 1997 onwards.

2.54

On this basis, this would suggest that a total long-run contribution of around zeroto the wedge between RPI and CPI inflation might be plausible as a result ofdifferences in the weights (Chart 2.8).

2.55

If we were to also take into account alternative average annual rates for financial
services and transport insurance (based on an average since 2003 for financial
services and an average excluding the period from 2009 onwards for transport
insurance) this would, for example, imply a total contribution of around -0.1
27

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Decomposing the differences in the RPI and CPI

percentage points to the wedge between RPI and CPI inflation due to differencesin weights.
2.56

However these adjustments are judgemental and any number of these could beapplied to each component. For the basis of the long-run assumption we thinkthat it is sensible to take a general approach using the average annual rate since1997 for all series, with the exception of clothing. On this basis, this would
suggest that a plausible total long-run contribution would be around zero to thewedge between RPI and CPI inflation, as a result of differences in the weights.

Working paper No. 2: The long-run
difference between RPI and CPI inflation28

3

Prospects for the long-term
wedge between RPI/RPIX
and CPI inflation

3.1

One way to assess the prospects for the long-term wedge between RPI and CPI
inflation is to look at the average contributions from each of the four main
components of the wedge over the past (the formula effect, housing components,
other differences in coverage and differences in weights). However there are anumber of limitations associated with using the long-term trend for contributions
to the wedge from each of the main components. The data since 2005 are notnecessarily comparable with the data from 1997 which were based on a previous
methodology for calculating contributions to the wedge. A bottom-up approachhas been used wherever possible here, looking at individual components which
are the key drivers of particular effects. These approximate calculations can thenbe used as a check on our long-term assumptions for the wedge between RPI and
CPI inflation.

3.2

The OBR previously assumed that the formula effect would contribute around 0.5
percentage points to the long-run wedge between RPI and CPI inflation,
consistent with the average contribution from the formula effect over the past. The
OBR’s March 2011 forecast was based on the assumption that the recent rises in
the formula effect will begin to stabilise and that the larger contribution from theformula effect in 2010 will persist. We assumed in March that the formula effectwill account for around 0.8 percentage points of the difference between RPI and
CPI inflation rates in the long run.

3.3

At the beginning of 2011, the formula effect has increased yet further, remaining
at around 1 percentage point from February to October 2011. One possibility is
the formula effect could continue to contribute a larger amount to the wedge
between RPI and CPI inflation in the long run. Future inflation data will continue
to be important in indicating the persistence of the recent increases in the formulaeffect.

3.4

Based on the data that is currently available (i.e. notwithstanding the outcome of
the ONS review of methods used to measure clothing inflation), the contribution
from the long-term formula effect could be higher than 0.8 percentage points
and fall somewhere in the region of 0.8 to 1 percentage points. In the long run,we think that it is plausible to assume that the formula effect contributes around29

Working paper No. 2: The long-run
difference between RPI and CPI inflation

Prospects for the long-term wedge between RPI/RPIX and CPI inflation

0.9 percentage points in our November EFO, which is the mid-point of thisrange.
3.5

The contribution from housing depends on developments in the housing market,
which has tended to drive a good deal of the volatility in the size of the wedge inthe past. In the long run we expect the housing market to grow broadly in linewith average earnings growth. A plausible assumption for the combined long-run
contribution to the wedge from housing components in the RPIX, such as housing
depreciation and council tax is around 0.35 percentage points.

3.6

In the long run, we expect mortgage interest payments (MIPs) to grow in line withaverage earnings growth of 4.7 per cent. This suggests that a plausible long-term
contribution of MIPs to the wedge between RPI and CPI inflation is around 0.15
percentage points.

3.7

Previously, a large contribution to the coverage component has come from themeasurement of car prices. If the divergence between purchases of vehicles priceinflation in the RPI and CPI since 2002 were to continue, this could contributearound -0.1 percentage points to the long-run wedge between RPI and CPI
inflation. The average difference in contributions from this component to RPI and
CPI inflation since 1997, as well as from 1997 to 2008, is around -0.1
percentage points. However it seems likely that the inflation rates for the twoseries will re-converge to something approaching their previous degree ofcorrelation, as used car prices cannot fall indefinitely and we might therefore
expect the two series to move together over time.

3.8

The Consumer Prices Advisory Committee (CPAC) has recommended to the UK
Statistics Authority that a single measure of new car prices should be used forboth the CPI and RPI. These changes are subject to the usual procedure for
introducing changes into the RPI, so the Bank of England will be consulted. A
public consultation is also taking place on these proposals. If agreed, thechanges are currently scheduled to be implemented in February 2012 and would
eliminate any differences in coverage as a result of the treatment of new car
prices in the RPI and CPI.

3.9

A bottom-up approach discussed here, which roughly decomposes thedifferences in weights by component acts as a good check on our long-term
assumptions. The approximations presented, as well as an additional assumption
for the clothing and footwear component suggests a contribution of around zerowould be plausible due to differences in weights.

3.10

Table 3.1 summarises a range of plausible assumptions for each component. For
the basis of our November EFO, we assume that the long-run difference between

Working paper No. 2: The long-run
difference between RPI and CPI inflation30

Prospects for the long-term wedge between RPI/RPIX and CPI inflation

RPI and CPI inflation is around 1.4 percentage points. This represents the midpoint of the plausible range of estimates.

Table 3.1: Plausible range of assumptions for the wedge between RPI and
CPI inflation
Plausible range of assumptions for the wedge between RPI and CPI inflation (percentage points)
Low
High
Formula effect0.8
1.0
Housing (ex. MIPs)
0.35
0.35
Coverage
0.0
0.0
Differences in weights
0.0
0.0
Total RPIX-CPI wedge
1.15
1.35
MIPs
0.15
0.15
Total RPI-CPI wedge
1.3
1.5

Risks and uncertainties
3.11

The work of the Consumer Prices Advisory Committee (CPAC) to adjust the CPI to
include owner-occupied housing costs and the method used may have asubstantial impact on the CPI and remains a risk to the prospects for the wedge
in the long run. The ONS is currently developing owner occupiers’ housing costs(OOH) indices using the net acquisitions (NA) and rental equivalence (RE)approaches for the potential inclusion in the CPI. 1

3.12

The NA approach treats a house as the purchase of a good which is partly anasset (the land) and partly consumable (the house). The cost associated withbuying and maintaining a house is considered as well as changes to the price ofthe house. However it is not currently possible to separate the cost of the housefrom the cost of the land. The RE approach assumes that there is a flow ofservices such as shelter and security of tenure which are consumed. The value ofthe services is assumed to be the same as the rent the house might attract in therental market. Owner occupiers’ housing costs are therefore imputed using therents paid for equivalent rented properties.

3.13

The choice of approach could have a material impact on the wedge between RPI
and CPI inflation. The NA approach, for example, would reduce the wedge
bringing a measure of CPI which includes OOH more in line with a measuresuch as RPIX excluding council tax. The use of a RE methodology would, on the1Consumer Prices Advisory Committee, September 2011, Annual Report to UK Statistics Authority.

31

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other hand, not have a substantial effect on CPI inflation and would therefore
mean that there would not be large changes to the wedge going forwards.

Working paper No. 2: The long-run
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32

A Coverage of inflation indices

Table A.1: Coverage of RPI, RPIX and CPI inflation indices
Housing coverage
Mortgage interest payments (MIPs)
House depreciation
Council tax
Rents
Building insurance and ground rentHouse transaction costs e.g. estate agents’ fees,
surveyors costs and conveyancing fees
Other coverage
Trade union subscriptions
Vehicle excise duty (VED)TV licence fees
Unit trust and stockbroker fees
University accommodation fees
Foreign students’ university tuition fees
New car prices
Population coverage
Highest earning households (top 4 per cent ofhouseholds by income)Institutional households
Pensioner households with ¾ of their income comingfrom state pensions and benefits
Spending by foreign visitors to the UK
Spending by UK households abroad

33

RPI

RPIX

CPI

√
√
√
√
√
√

√
√
√
√
√

√

√
√
√

√
√
√
√
√
√
√
√
√
√
√

√

√

Working paper No. 2: The long-run
difference between RPI and CPI inflation

C

Working paper No. 2: The long-run
difference between RPI and CPI inflation34

B ONS methodology formeasuring the RPI-CPI
wedge

B.1

The ONS has produced a revised methodology for the breakdown of thedifference between RPI and CPI inflation from January 2005 onwards. The
revised methodology is a ‘contributions’ approach which gives an estimate of theeffect of a particular component on the annual rate of CPI or RPI inflation. By
comparison, the previous methodology ran from 1997 to May 2010 and was
calculated by using annual changes and adding/subtracting them from theheadline rates to calculate each component. 1

B.2

Based on a comparison of the two methodologies in the period that they overlap
from January 2005 to May 2010 (Table B.1), housing (in particular ‘otherhousing’ excluding MIPs) contributes a larger amount to the wedge using therevised methodology. Similarly, other differences in coverage contribute slightly
more using the new method. Revisions to both of these components are offset bya lower contribution from differences in weights resulting in an unchanged wedge
between RPI and CPI inflation (see Charts B.1 to B.7).

B.3

Table B.2 shows a comparison of the averages for each of the components using
a combined series (the previous methodology up to 2005 and the revised
methodology up to the latest data in October 2011) compared to the average ofthe series based on the new and previous methodologies separately. In general,
it is possible that if the ONS was to extend the new methodology back so that theseries began in 1997, then compared to the combined series, the averagecontribution from housing could be larger, whereas there could be lower
contributions from differences in weights.

1

See ONS Information Note: Consumer Prices Index and Retail Prices Index – analysing differences.

35

Working paper No. 2: The long-run
difference between RPI and CPI inflation

ONS methodology for measuring the RPI-CPI wedge

Table B.1: Comparison of previous and revised methodologies over theperiod they overlap
Previous method
2005-May 2010
0.3
-0.2
-0.2
0.0
0.5
-0.2
0.2

RPI-CPI
Housing, of which:
MIPS
Other housing
Formula effect
Other difference in coverage
Differences in weights

Revised method
2005-May 2010
0.3
0.3
0.0
0.3
0.5
-0.1
-0.4

Difference
0.0
0.5
0.2
0.3
0.0
0.1
-0.6

Table B.2: Comparison of averages over the series using the previous andrevised methodologies

RPI-CPI
Housing, of which
MIPS
Other housing
Formula effect
Other difference incoverage
Differences in weights

Previous
method1997-May
2010
0.9
0.4
0.0
0.4
0.5

Previous
method1997-2005
1.2
0.8
0.2
0.6
0.5

Revised method
2005-October
2011
0.5
0.3
0.0
0.3
0.6

Combined1
1997-October
2011
0.9
0.5
0.1
0.5
0.6

-0.1

-0.1

-0.1

-0.1

0.1

0.0

-0.3

-0.1

1

The previous methodology is used from 1997 to 2005 which is combined with the revised methodology from 2005 to

October 2011to form a longer time series.

Working paper No. 2: The long-run
difference between RPI and CPI inflation

36

ONS methodology for measuring the RPI-CPI wedge

Chart B.1: Contribution from formula effect
1.1
1Percentage points

0.9
0.8
0.7
0.6
0.5
0.4
0.3
1997

1999

2001

2003

2005

Previous methodology

2007

2009

2011

2009

2011

Formula effectSource: ONS

Chart B.2: Contribution from housing components
32Percentage points

1
0
-1
-2
-3
-4
1997

1999

2001

2003

2005

Previous methodology

2007
Total housing

Source: ONS

37

Working paper No. 2: The long-run
difference between RPI and CPI inflation

ONS methodology for measuring the RPI-CPI wedge

Chart B.3: Contribution from housing components excluding MIPs
1.5

Percentage points

1
0.5

0
-0.5

-1
-1.5
1997

1999

2001

2003

2005

Previous methodology

2007

2009

2011

2009

2011

Other housing

Source: ONS

Chart B.4: Contribution from MIPs
2
1.5
1
Percentage points

0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
1997

1999

2001

2003

2005

Previous methodology
Source: ONS

Working paper No. 2: The long-run
difference between RPI and CPI inflation

38

2007
MIPs

ONS methodology for measuring the RPI-CPI wedge

Chart B.5: Contribution from other differences in coverage
0.4
0.3

Percentage points

0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
1997

1999

2001

2003

2005

2007

Previous methodology

2009

2011

Differences in coverage

Source: ONS

Chart B.6: Contribution from differences in weights
1.5

Percentage points

1

0.5
0
-0.5

-1
-1.5
1997

1999

2001

2003

Previous methodology

2005

2007

2009

2011

Differences in weights

Source: ONS

39

Working paper No. 2: The long-run
difference between RPI and CPI inflation

ONS methodology for measuring the RPI-CPI wedge

Chart B.7: Differences between RPI and CPI inflation based on the two
methodologies
32Percentage points

1
0
-1
-2
-3
-4
1997

1999

2001

2003

2005

2007

Previous methodology

2009

2011

RPI-CPI

Source: ONS

Table B.3: Contributions to the difference in RPIX/RPI and CPI inflation
rates

Formula effect2
Since 19973
Housing (ex. MIPs)
Since 1997
Other differences in coverage
Since 1997
Other differences inc. weights
Since 1997
Total RPIX-CPI wedge4
Total RPIX-CPI wedge since 19974
MIPs
Since 1997
Total RPI-CPI wedge4
Total RPI-CPI wedge since 19974

Current1

Average

Minimum

Maximum

1.0

0.6
0.6
0.3
0.5
-0.1
-0.1
-0.3
-0.1
0.6
0.9
0.0
0.1
0.5
0.9

0.4
0.4
-0.6
-0.6
-0.3
-0.4
-1.0
-1.0
-0.8
-0.8
-2.8
-2.8
-3.5
-3.5

1.0
1.0
1.0
1.3
0.2
0.3
0.2
0.4
1.8
1.8
1.5
1.5
2.3
2.6

-0.1
-0.2
-0.3
0.6
0.0
0.4

1

Standard
deviation
0.2
0.1
0.4
0.4
0.1
0.1
0.3
0.3
0.6
0.5
1.1
0.9
1.5
1.2

October 2011
The average, minimum, maximum and standard deviation are calculated from Jan 2005 to October 2011. The ONSchanged the methodology which it uses to calculate the contributions to the wedge, designed to provide a moreaccurate breakdown. Data using the revised methodology begins in 2005.
3
The average, minimum, maximum and standard deviation are based on a combined series which uses data from1997 to 2005 based on the old methodology used by the ONS and the data from 2005 onwards using the new
methodology.
4
The components may not sum to the total wedge between RPI/RPIX and CPI, as the total wedge is calculated using
published RPI, RPIX and CPI inflation rates rounded to 1 decimal place.
2

Working paper No. 2: The long-run
difference between RPI and CPI inflation

40

ONS methodology for measuring the RPI-CPI wedge

41

Working paper No. 2: The long-run
difference between RPI and CPI inflation