The ONS announcement can be read online.

The decision follows the conclusion of an independent public statistical consultation held last year by the ONS into the means to correct the increasing disparity between inflation estimates produced by the RPI and the Consumer Price Index (CPI). The disparity has been largely due to what has been called the formula effect since while the CPI makes extensive use of the Jevons method to average price changes the RPI uses the Carli and Dutot methods method. The ONS has decided to keep the existing RPI to maintain continuity for existing users and so for the present the £362 billion index-linked gilt edged securities market will remain indexed to the RPI. There had been accusations that a change in formula, which would reduce RPI estimates down closer to those of the CPI, providing a substantial saving to the cash-strapped British government, was politically motivated. The decision to produce a new index, the RPIJ, instead of changing the formula for the RPI looks suspiciously like a failure of political will. , World Economics' /> The ONS announcement can be read online.

The decision follows the conclusion of an independent public statistical consultation held last year by the ONS into the means to correct the increasing disparity between inflation estimates produced by the RPI and the Consumer Price Index (CPI). The disparity has been largely due to what has been called the formula effect since while the CPI makes extensive use of the Jevons method to average price changes the RPI uses the Carli and Dutot methods method. The ONS has decided to keep the existing RPI to maintain continuity for existing users and so for the present the £362 billion index-linked gilt edged securities market will remain indexed to the RPI. There had been accusations that a change in formula, which would reduce RPI estimates down closer to those of the CPI, providing a substantial saving to the cash-strapped British government, was politically motivated. The decision to produce a new index, the RPIJ, instead of changing the formula for the RPI looks suspiciously like a failure of political will. , World Economics' /> The ONS announcement can be read online.

The decision follows the conclusion of an independent public statistical consultation held last year by the ONS into the means to correct the increasing disparity between inflation estimates produced by the RPI and the Consumer Price Index (CPI). The disparity has been largely due to what has been called the formula effect since while the CPI makes extensive use of the Jevons method to average price changes the RPI uses the Carli and Dutot methods method. The ONS has decided to keep the existing RPI to maintain continuity for existing users and so for the present the £362 billion index-linked gilt edged securities market will remain indexed to the RPI. There had been accusations that a change in formula, which would reduce RPI estimates down closer to those of the CPI, providing a substantial saving to the cash-strapped British government, was politically motivated. The decision to produce a new index, the RPIJ, instead of changing the formula for the RPI looks suspiciously like a failure of political will. , World Economics' />

Calculating UK inflation: Common Sense or Common Theft

Brian Sturgess - December 2012


A seemingly innocuous decision by a statistical agency to reconsider the method of calculation of an index of consumer price inflation is developing into a political minefield with accusations of government manipulation and pressure.  This is happening not in Argentina, where it is widely accepted that the Government’s official inflation measure vastly underestimates rises in the cost-of-living, but in the United Kingdom.  At a public meeting held in London on October 26, 2012 attended by the author, accusations of facilitating a politically motivated agenda were levelled against the Office of National Statistics (ONS).

The controversial meeting resulted from an independent public statistical consultation launched on September 18, 2012 by the ONS into the methodology used to calculate the Retail Price Index (RPI). The RPI was once the principal means of calculating consumer price inflation and the cost of living until superseded by the Consumer Price Index (CPI) in 2003. [1]  The two indices have continued to coexist and although a number of user groups have switched from the RPI to the CPI since the government changed its inflation targeting regime to the new inflation measure, others have stayed with the RPI. For example, despite the move to use the CPI instead of the RPI as an inflation target, the UK government confirmed that index-linked gilts, public sector pensions and benefits would remain indexed to the RPI.  The latter two along with tax credits moved to CPI indexation in April 2011, but the £362.4 billion index-linked gilt market remains tied to the RPI. [2] Meanwhile, the RPI is used for indexation by many private sector pension schemes, for calculating the real interest on student loans, for pay bargaining and in many other contracts. [3]

The continuing coexistence of officially sanctioned inflation measures, rather than the clean replacement of one method, by another one allows for the possibility of introducing distortions in economic decisions over time arising from differing ways of measuring consumer price inflation. These distortions occur as long as different user groups use alternative measures of inflation and that these measures do not produce the same estimates.  This arises simply because decisions and contracts aimed at real, rather than nominal, valuations will not be made on estimates of the same rate of inflation. For example, if the RPI is greater than the CPI then adjusted payments aimed at maintaining the real standard of living of pensioners will relatively disadvantage retired public sector workers. A CPI inflation estimate higher than the RPI would relatively disadvantage private sector pensioners. Two official indices with different user groups, therefore, produce serious distributional effects.[4]

Unfortunately, for some time the inflation estimates generated by the RPI and the CPI have not given the same result and in some periods the differences have been quite large. This is shown in Chart 1 which shows the monthly changes in the annual inflation rate estimated by the RPI and the CPI over the period January 2001 to July 2012.  Some difference would be expected between the two inflation estimates since the RPI and the CPI vary in the coverage of the commodities whose prices are surveyed and in the population groups covered. The CPI is calculated on the basis of the expenditure patterns of a wider section of the population than the RPI which excludes high and low income groups. The CPI excludes owner occupier’s housing costs and is based on a narrower range of commodities than the RPI. However, an important part of the differences observed between them has been due to different approaches to the averaging of prices: the so-called formula effect. The formula effect has been growing in importance driving a wedge between the two measures of inflation. According to Ellis (2012) [5] “at  the time of the change in the Bank of England’s inflation target from RPIX to CPI, the formula effect had accounted for around 0.5 percentage points (ppts) of the difference between the two inflation measures. Since then, its impact has become much more pronounced. The ONS estimates that the formula effect caused the RPI to be 0.88 percentage points higher than the CPI in September 2012, just before the public consultation was launched.

 

 

The Formula Effect

The formula effect arises from the process of trying to measure price changes at the most basic levels of commodities termed ‘elementary aggregates’. Elementary aggregates are collections of relatively homogenous goods and services such as bananas, rice, haircuts etc. and the price sample of these items may cover parts of the country or the entire country or type of outlet.

The final choice of the relatively small number prices sampled of these elementary aggregates is a compromise between a number of practical factors, but the selection made by the ONS is meant to be representative of a set of similar goods that are expected to have similar price movements so that the range of price movements within the elementary aggregate category is minimised. The crude, but unverified theory behind this is based on the concept of substitutability between the items chosen for an elementary aggregate sample.  [6] The ONS also tries to choose items that are expected to remain in the market for a long time.  

Data are not generally available for weighting purposes on the proportion of consumer expenditure spent within an elementary aggregate so in order to estimate inflation at the most basic level price changes within these groups are averaged using an ‘unweighted’ approach.  There are many formulae for calculating price indices using unweighted basic price data, but most statistical institutes across the world choose between, or combine, two of them, the Dutot, [7] which is an arithmetical average of price data, or the Jevons,[8] which is a geometric average of prices.

The Jevons formula is the method used by the ONS in the calculation of most of the unweighted averages of the CPI. In the UK another formula the Carli [9] is also used in the calculation of the RPI alongside the Dutot, but the Jevons method is not employed. European regulations only permit the use of the Carli formula in calculations of price indices such as the CPI under certain restrictive assumptions.  

The current use made of the different formulae by the ONS in the calculation of the CPI and the RPI is shown in Table 1. It shows that while 63% of the unweighted first stage price averaging in the calculation of the CPI is undertaken using the Jevons formula, the CPI also used the Dutot for 5% of calculations, while the RPI used it for 29% of them in the first stage of aggregation. The Dutot formula is used for averaging the prices of relatively tightly defined items such as alcohol and tobacco.  The Carli formula in the calculation of the RPI is used for categories of expenditure where wider price variations arise from broader descriptions of items such as furniture and clothing sectors. Since such wide price differences limit the application of the Dutot formula, the ONS has used the Carli for around 27% of the first stage of aggregation in the calculation of the RPI.

 

 


Why does the formula effect matter?

A simple example can demonstrate why the formula effect matters. If prices are sampled from two goods – tomatoes and bananas and in October tomatoes cost 200p and bananas cost 100p. If in November, the price of bananas rises to 150p and the price of tomatoes falls to 150p, what is the rate of inflation?  Since these goods are elementary aggregates inflation must be calculated by one or other of the set of formulae for calculating unweighted averages of a group of prices.

Inflation is zero between the two periods according to the Dutot method since the average (arithmetic mean) price level in November at 150p is exactly the same as the price level in October. According to the Carli method the rate of inflation is based on the arithmetic average of the two price relatives – the change in the price relatives between the months which is 1.50 for bananas and 0.75 for tomatoes. In order to calculate the Carli rate of inflation, it is necessary to take the arithmetic average of these price relatives, multiply by 100 and subtract 100 giving a rate of inflation of 12.5%.  In contrast, calculating inflation by the Jevons formula involves taking the geometric average of the two price relatives (the square root of their product for two goods, the cube root for three and son on), multiplying by 100 and subtracting 100. The inflation rate measured by the Jevons method is 6.1%. So three different formulae for estimating the rate of inflation on the same price data produces three very different estimates for the rate of inflation. This is shown in Table 2.

 


This has a significant economic impact. To take an extreme example, a pensioner whose income was Dutot indexed with an income of £100 per month in October would still receive a £100 a month in November, but if that pensioner consumed only bananas, she would be able to buy 100 of them in October, but only 67 a month later. This represents a real fall in income. Admittedly, she could buy 16 more tomatoes a month, but such substitutions across a wide range of goods in reality are less feasible and are more unlikely. Alternatively, a Carli index linked pensioner would receive enough extra money to buy an extra 12 bananas while a Jevons pensioner could buy an extra 6. Obviously, the pensioner could buy more tomatoes to compensate for the fewer bananas, but the realism of this basic question of substitutability is important since pensioners spend more on goods such as energy which rise relatively more in price than average and less on goods which fall in price such as computers. Their real standard of living is reduced by some price rises more than would be predicted by official inflation figures based on price averaging among a large set of elementary aggregates.

 

The formula effect has caused particularly serious problems in the clothing and footwear sector where the Jevons is used in the calculation of the CPI and the Carli is used in the RPI. In 2011, clothing and footwear inflation was 2.3% measured by the CPI, whereas the RPI recorded a rise of 11.5% in prices. In August of 2012, the RPI recorded annual inflation of 6.1% whereas the CPI showed deflation of 0.7% all on the same price data. The importance of this issue is the impact of differences in inflation estimates in clothing and footwear on the all item price indices due to a difference in formula. The ONS has noted that this “difference is the primary cause of the formula effect, which was relatively stable at around 0.5 percentage points on the annual growth rate until changes were introduced to the collection guidelines for clothing in 2010.”[10] The changes were intended to improve the quality of price collection data in the diverse clothing sector, but ended up widening the impact of the formula effect on all items to around a 1.0 percentage point.

 

 

 

The ONS launches its consultation process

The Consumer Price Advisory Committee (CPAC) of the ONS has been investigating the formula effect since late 2010. This was one of two priorities for the future development of prices statistics[11] The decision to consult the public about the formulae used in the calculation of the RPI was taken by the National Statistician, Jil Matheson, the government’s principal adviser on official statistics. The ONS received advice from various experts including Professor Erwin Diewert of the University of British Columbia who recommended that the ONS should drop its use of the Carli index as an elementary index in the RPI and replace it by either the Jevons index or the Carruthers Sellwood Ward and Dalen (CSWD) elementary index. [12] Based on this advice the ONS published a discussion document on its website to facilitate the consultation process.

According to this document which formed the basis of the presentations at the public meeting held in London the ONS is seeking the public’s views on four options: 1) no change; 2) change the approach of averaging prices for one category, such as clothing and footwear, 3) change the approach for all categories, 4) align the RPI formulae with the CPI approach. 

The consultation process closed on 30 November and the CPAC will meet and make recommendations for change to be considered by the UK Statistics Authority Board. The Bank of England will also be consulted as to whether a fundamental change in the method of calculating the RPI “would be materially detrimental to the interests of holders of each relevant index-linked gilts.”[13] If there are no issues the Chancellor of the Exchequer’s consent would be required and the revised RPI would be first published on 19 March 2013. Some participants in the public meeting regarded this process as almost indecent haste.

 

Independent Consultation or Political Pressure

The main substantive complaint against the consultation process, co-ordinated by Derek Bird, Head of Prices Division at the ONS, but undertaken in response to the National Statistician is that it is not an independent process at all, but instead that it has been launched in response to government pressure with the ultimate aim of reducing the calculated value of the RPI to a level close to that of the CPI. Bird insists that it merely invites views on the statistical merits of a range of options, one of which is no change and that there is no predetermined outcome.

 The simplest and the most radical move would have been to completely replace the RPI with the CPI for all government commitments, including index-linked gilts, in 2003 when the RPI was dropped for inflation targeting, This was not done and the lack of political courage at that time has allowed economic distortions to accumulate from having two official measures of consumer price inflation. The extension of the application of the CPI to public sector pension scheme liabilities announced in July 2010 and executed in April 2011 also exempted index-linked gilts although in June 2011 the Debt Management Office published a consultation document on whether to issue CPI-linked gilts.[14]

The government cannot politically switch all outstanding index-linked gilts from the RPI to the CPI without facing widespread accusations of breaking contracts and even expropriation. It can, however, affect the relative pay-offs made to holders of index-linked gilts compared to other financial assets by adjusting the estimates of RPI inflation so that it is closer to the return on CPI indexed-assets. A partial or a full elimination of the formula effect which has driven the wedge between the RPI and the CPI would produce such a result. This would significantly reduce the debt interest payments of the Treasury, but it would also have an impact on the current market value of index-linked gilts. It has been estimated by one fund manager that a typical index-linked gilt stock, the 4.125 per cent 2030, would lose 43% of its market value if the differences between the rate of inflation on the CPI and the RPI were removed. [15] At the public meeting held by the ONS in October pension fund representatives were particularly disturbed by this possibility. 

This means that Option 4, a full alignment of the RPI and the CPI may not be politically feasible, but the government would still save money on Options 2 and 3, since even applying Jevons to clothing would remove a large part of the formula effect. Limited reform would also reduce the pension liabilities of private sector companies who are still tied, unlike the public sector, to indexation through the RPI. Option 1, no change, would make it difficult for the government to stimulate the market’s appetite for an eventual introduction of CPI-linked gilts since the outstanding stock of RPI gilts would remain relatively more attractive as an inflation hedge for some time. This would dampen down investor interest in the first issues of CPI gilts, but a reduction in the formula effect would raise the degree of substitutability between them.

The ONS rejects the accusations that there is a political agenda. Indeed at the public meeting attended by the author the ONS repeatedly stressed that it was a body with integrity and not a ‘patsy’ of politicians and that the consultation process had arisen internally as a result of the adverse impact of the 2010 clothing sector changes. The ONS repeatedly claimed that it simply wished to reduce bias in the measurement of consumer price inflation caused by the formula effect.

The question of bias itself is interesting because the real rate of inflation, unlike the boiling point of water in a vacuum, is not something that has a real, as opposed to a conceptual existence. The extent to which an estimator of the rate of inflation exhibits an upward or a downward bias is only meaningful in comparing one index against another since there is no actual rate of inflation outside of simple macroeconomic models. Inflation in terms of rising prices is an observable phenomenon, but the rate of inflation is what the philosopher John Searle terms an institutional fact, or one which exists as a result of collective recognition.[16]  In this respect, the ONS has taken and publically declared it in the meeting, that the CPI represents as close as possible the true rate of inflation given that it was the ‘state of the art’ making an extensive use of the Jevons formula. The ONS also noted that few countries use the Carli and in a European survey they could only find Slovenia mimicking the United Kingdom in its dual system of inflation measurement with an outdated formula.

Conceptually, there is nothing wrong with a regime of competing measurements of inflation. Indeed, given that there is no true catch-all rate of inflation and that price changes have distributional effects, many indices might be more efficient. The problem arises from tying government contracts and payments to an official rate and the unwarranted defence of this rate on ‘scientific’ grounds whether it is the RPI or the CPI. This situation produces the potential at best for distorted decision-making and at worst for political abuse. 

 



[1] The RPI was introduced in 1947 and was made the official inflation measure in 1956.  The CPI was introduced in 1996 in response to European Union regulations and was made the foundation of the government’s inflation target in 2003 replacing the RPI excluding mortgage payments (RPIX) which had been the target since 1992.

[2] The index linked market size is regularly updated on the UK governments Debt Management Offic’s website, http://www.dmo.gov.uk/reportView.aspx?rptCode=D1D&rptName=2556979&reportpage=D1D

[3] The RPI is also used for price regulation in particular for train fares and other privatised utilities.

[4] The problem caused by the existence of two official estimates of inflation is separate from, but additional to, any theoretical money illusion distortions arising from unobservable, but experienced variations between real underlying inflation and measured inflation. If real inflation is higher than anticipated inflation then negative income and wealth effects will be experienced. If it is lower, then these unanticipated effects arising from forecasting mistakes will be positive. an in-built having different measurements can aggravate such mistakes raising decision makers learning costs. These costs are exacerbated if the inflation measures used are significantly different, but they are minimised the closer the correlation between them.

 

[5] Colin Ellis, Measuring UK Inflation, Practical Issues and Difficulties, World Economic Volume 13, 4, September-December 2012

[6] The question of the importance of substitutability between goods included in elementary aggregates is debatable. To what extent is a haircut in London a substitute for on in Wick or how substitutable is a knife with a spoon?

[7] The Dutot formula was developed in 1738 by the French economist Dutot. It creates an index calculated by dividing the average price in period t by the average price in period t-1.

[8] The Jevons formula was developed by the English economist Jevons in 1863. It is the geometric average of the price relative of period t to period t-1.

[9] The Carli formula developed in 1764 by the Italian economist Carli and it is calculated by the arithmetic average of the price relative, or ratio, between period t and period t-1.

[10] See Options for improving RPI consultation document, ONS, October 2012, p10., http://www.ons.gov.uk/ons/about-ons/user-engagement/consultations-and-surveys/national-statistician-s-consultation-on-options-for-improving-the-retail-prices-index/index.html

[11] The other priority was the inclusion of owner occupiers’ housing costs in a new additional measure of inflation. The consultation for this issue closed on 31 August 2012.

[12] Erwin Diewert Report on Consumer Price Statistics in the UK http://www.ons.gov.uk/ons/guide-method/user-guidance/prices/cpi-and-rpi/index.html

[13] See Options for improving RPI consultation document, ONS, October 2012, p24, http://www.ons.gov.uk/ons/about-ons/user-engagement/consultations-and-surveys/national-statistician-s-consultation-on-options-for-improving-the-retail-prices-index/index.html

[14] CPI-linked Gilts: A Consultation Document, United Kingdom Debt Management Office, 29 June 2011. http://www.dmo.gov.uk/documentview.aspx?docname=/publications/giltsmarket/consultationpapers/cons20110629.pdf&page=consultation.

[15] RPI revamp risks ‘ruining’ linker returns, Financial Times, 3 June, 2012,

 http://www.ft.com/cms/s/0/8ef07ff0-ab2c-11e1-b875-00144feabdc0.html#axzz2CxLQzxui

[16] According to Searle an  institutional fact (a) cannot exist unless a community collectively accepts it as existing; (b) requires the assignment to an entity of a "status function" (that is, of a function that an entity can only have by virtue of collective recognition, and not merely by virtue of whatever properties it might have prior to such recognition); and (c) characteristically generates, once in existence, "deontic powers" (in particular, rights and obligations) within the community whose behaviour brings it to existence.