RPI/CPI User Group

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To foster co-operation and the exchange of information between the ONS, its advisory bodies and other users. Please see 'Aims of the RPI/CPI User Group' in the library for further details.

The debate over the Retail Prices Index

  • 1.  The debate over the Retail Prices Index

    Posted 02-02-2018 15:17
    Hi All

    This subject has reared what we might call its ugly head again and this time it was the Governor of the Bank of England Mark Carney doing so. From Sky News.

    "Bank of England governor Mark Carney has called for an end to the use of RPI - the discredited inflation measure still used to calculate rail fare hikes and student loan interest payments."

    This is interesting on two main grounds. One is that if he thinks RPI is so wrong and that is the Bank of England view why it has been used so long in its own pension scheme, partly for benefits but also as an investment vehicle? Also if the RPI has "no merit" as he states below why it has taken him from July 2013 to January 2018 to notice it?

    ""At the moment we have RPI, which most would acknowledge has no merit; we have CPI, which virtually everyone recognises and is in our remit; and we have the ONS favourite CPIH, which includes housing costs."

    Sadly his rhetoric is both disappointing and typical as the RPI certainly has merits as for example unlike CPI it covers owner-occupied housing and unlike CPIH it does so without having to use fantasy economics and statistics. You may also note that he is not exactly praising CPIH.

    On the upside at least he has mentioned the subject as up until now he has been both supine and silent on the changes to the inflation remit in his term of office.



  • 2.  RE: The debate over the Retail Prices Index

    Posted 02-02-2018 18:38
    It is not just the BoE pension scheme which is RPI linked.  There is still a large number of private schemes hard-linked to the RPI.

    Recently, British Telecom tried to move some of its pension holders from an RPI linked to a CPI linked scheme.  They were challenged in court and lost.  If RPI is written into the pension contract it cannot be changed without a general legal change by the government.

    Some of the people entering these RPI linked schemes are very young, so it is difficult to see any justification for discontinuing the RPI for 50 to 100 years.


  • 3.  RE: The debate over the Retail Prices Index

    Posted 03-02-2018 03:44

    Hello, Shaun:

    I will add a document to the library tomorrow, "Governor Carney's Evidence on Consumer Price Indices before a Parliamentary Committee" that gives my views on the matter.

    I added a comment on your January 31 blog that reads in part: "Chris Giles [of FT] was mistaken in reporting Carney as saying "most would acknowledge, [the RPI] has no merit" …. What he actually said, audible on the tape even if he is a mumbler, is: "At the moment, we have RPI, which most would acknowledge has known errors."

    Far more inexplicable than Governor Carney's silence on the RPI is his silence on RPIJ, which to my knowledge has never been broken. Most of his public career, at the Bank of Canada and at the Department of Finance, he supported without a single caveat the Canadian CPI as the target inflation indicator of the Bank of Canada, an index that is very close methodologically to the RPIJ. It has much less in common with the UK CPI or the CPIH. If he really finds the accounting approach to measuring owner-occupied housing costs used in the RPI/RPIJJ lacking why did he have no problem with it in almost a decade in Canadian public life, since the Canadian CPI uses the same approach? Like everyone else, he is entitled to change his mind, but if this is what has happened he surely owes an explanation to the UK public when and why this happened.

    Happy Groundhog Day! (Wiarton Willie saw his shadow so we will have at least six more weeks of winter here.)


  • 4.  RE: The debate over the Retail Prices Index

    Posted 03-02-2018 11:54
    Edited by Arthur Barnett 03-02-2018 12:17

    A big thank you to Andrew for pointing out the error in Chris Giles account which prompted me to look again at the committee web site.


    The Lords Committee has now published the text of Mark Carney's evidence which is easier to follow. http://data.parliament.uk/writtenevidence/committeeevidence.svc/evidencedocument/economic-affairs-committee/governor-of-the-bank-of-england-2017/oral/77776.pdf


    The evidence on price indices starts on page 19 with a question from Lord Livermore.


    Mark Carney's opening paragraph is recorded as follows –


    "Well, there are, as you say, some known errors, acknowledged by the ONS and recognised by a number of external commentators. We would share some of those views about how the index is calculated, using the Carli method, which has an asymmetric bias, and how housing costs are implemented, as well as issues about clothing. So there are some known errors."


    I won't comment further here other than to say that there are issues around all these "known errors".


    All the best.



  • 5.  RE: The debate over the Retail Prices Index

    Posted 22-02-2018 11:46
    Hi All

    Thank you to Andrew and Arthur for their replies, thoughts and insight on this matter. I decided to send my views on this important issue to Mark Carney the Governor of the Bank of England. They reflect the discussions on here but any responsibility is of course mine.

    Dear Governor

    I would like to return your attention to the evidence you gave to the Select Committee on Finance of the House of Lords on the 30th of January on the Retail Price Index or RPI. This is not only because it is an important matter it itself but also it is a welcome innovation to see the Bank of England enter the debate over how to measure inflation. However I do have concerns about what you said and in particular this section.

    "Well, there are, as you say, some known errors, acknowledged by the ONS and recognised by a number of external commentators. We would share some of those views about how the index is calculated, using the Carli method, which has an asymmetric bias, and how housing costs are implemented, as well as issues about clothing. So there are some known errors."

    The issue of "known errors" within the RPI is much more open to debate than you suggested and such debates have taken place at the Royal Statistical Society and it is a shame that the Bank of England has not engaged with these. It is also my understanding that its treatment of housing costs is analogous to that used by the CPI in Canada during your tenure as Governor of the Bank of Canada so are you now unhappy with the latter as well?

    By contrast if we move to the Consumer Price Index or CPI which is currently used as the UK inflation target measure there is a glaring hole in the way it completely ignores the owner-occupied housing sector. I am not sure what is a step up from known error but I can say that ignoring something as important to the UK as that sector when UK  house prices have risen by over 29% in your term as Governor when the targeted CPI has only risen by more like 7% is exactly that.

    Perhaps worst of all is the current favourite of the Office for National Statistics the inflation measure called CPIH and that is because it uses fantasy numbers to cover the housing sector. There is an obvious problem in assuming that owner-occupiers pay rent to themselves when they do nothing of the sort. This is added to by the problems seen with the data where after what was described as somewhat euphemistically as a "discontinuity" we are on what in film industry terms is called "take two". Also my understanding is that the ONS does not have full access to UK rents data as the problems with this measure multiply.

    You made no mention in your evidence of the Eurostat report that must be released before December 31, 2018 on the incorporation of an Owner Occupied or  OOH component  based on net acquisitions in Eurostat HICPs. If Eurostat did decide to incorporate such a component in Eurostat HICPs, it would mean, as things currently stand, that the remit of the Bank of England would be changed through the back door, as the UK CPI is just the UK HICP under another name. What is your view of Eurostat's proposed HICP reform via the use of house prices and the implications for UK inflation measurement and targeting?

    Furthermore there is the issue over how your words have been reported in the media and in particular over the use of the phrase "no merit" in relation to the RPI. This was reported to my knowledge by the Financial Times and Sky News.  Indeed the economics editor of the Financial Times Chris Giles has repeatedly emphasised the point across many different media forms. However the transcript which was kindly posted on the Royal Statistical Society website ( www.statsusernet.org.uk ) does not appear to contain this phrase. I would appreciate it therefore if the Bank of England would take the opportunity to put the record straight as otherwise there is the danger of misapprehension. 

    I await your thoughts in response.

    Kind Regards

    Yours Faithfully

    Shaun Richards


  • 6.  RE: The debate over the Retail Prices Index

    Posted 23-02-2018 14:09

    Dear Shaun:

    Good luck with your letter. I am sure you will receive some kind of response. And thank you for your kind acknowledgement of the help of Arthur and myself.

    As you say, the RPI's "treatment of housing costs is analogous to that used by the CPI in Canada" when Mr. Carney was the governor of the Bank of Canada (and actually for his whole public career in Canada at both the Bank of Canada and the Department of Finance). I would like to emphasize a point I made in my document "Governor Carney's Evidence on Consumer Price Indices before a Parliamentary Committee": the only important difference in scope between the two indices is that the Canadian CPI's basket includes land transfer taxes while the RPI's excludes stamp duties. Land transfer taxes are an important cost to homeowners in Canada just as stamp duties are in the UK. By coincidence they became substantially more important in Canada on February 1, 2008, the very day that Carney took office as governor, when Toronto, the largest Canadian city, introduced a municipal land transfer tax, making it the only city to have both a municipal and a provincial land transfer tax. So if Governor Carney disagrees with the treatment of OOH in the RPI, he should have disagreed even more strongly with the treatment of OOH in the Canadian CPI, since land transfer taxes are a transaction cost and a component of gross fixed capital formation.

    The Bank of England for many years calculated a Housing-Adjusted Retail Prices (HARP) Index based on the opportunity cost variant of the user cost approach. As you know, Gareth jones, in our RPI CPI User Group, is a strong advocate of this approach.  The HARP index excluded all transaction costs, not just stamp duties, but also estate agents' fees and conveyancing fees, quite reasonably so from the BoE's perspective, as these were all part of gross residential construction expenditures and were not part of consumption.

    The rental equivalence approach and the opportunity cost variant of the user cost approach are closely related and in fact they can always be made equivalent in empirical work simply by choosing an appropriate interest rate for the opportunity cost of owner's equity. In February 1993, the BoE preferred the opportunity cost approach because "rents in the controlled private market did not provide a good guide to the rental equivalent of owner-occupied houses", but the Bank of England no longer seems to have any concerns on this subject.  The rental equivalence approach has pretty much always treated transaction costs as out-of-scope wherever it has been implemented. They are not in the US CPI; neither are they included in the OOH component of the CPI.

    Recently a Bank of Canada paper proposed that the Canadian CPI switch from its accounting approach to measuring OOH, which for some reason they choose to consider a truncated opportunity cost approach, to a full-fledged opportunity cost approach:


    However, they have left all transaction costs in their proposed index: land transfer taxes, real estate commissions and legal fees. They are all part of the other owned accommodation expenses component. It is surely inappropriate to talk about measuring "the value of the services consumed" and be quite unfazed about including elements of gross residential construction expenditures in your measure but it doesn't seem to bother the authors of the paper so possibly it doesn't bother their former boss either.

    I hope that you do not have a long wait for a response to your  excellent letter.

    Best regards,




  • 7.  RE: The debate over the Retail Prices Index

    Posted 08-03-2018 13:36
    Hi All

    This morning the ONS has released yet another missive in its campaign against the RPI. To some extent that may be a response to requests at the last User Group meeting although in terms of the specific request I recall for a proper and full analysis of Carli methodology the quote below is not entirely reassuring.

    " It is possible to produce hypothetical scenarios in which any of the formulae can be shown to produce reasonable or unreasonable results."

    However I think that the most revealing sentence in the piece is the one below.

    " this means that the RPI is heavily influenced by house prices and interest rates, "

    So real prices are bad but Imputed ones such as Rents that owner occupiers never pay are good?


    Shaun Richards

  • 8.  RE: The debate over the Retail Prices Index

    Posted 11-03-2018 21:02

    Below are comments on a few of the issues with the section on the formula effect in the ONS article "Shortcomings of the Retail Prices Index as a measure of inflation". 


    These comments are for the most part based on evidence presented in previous posts on SUN.


    The formula effect section is in part factually incorrect and arguably in other parts misleading in its selective use of evidence though ONS do not appear to claim that this article represents any more than their judgement.


    The article is factually incorrect in associating transitivity and "price bounce" solely with the use of Carli in the RPI.  This price bounce argument would apply to a chain linked Carli index and the RPI methodology doesn't use chain linked Carl.  Chain linking occurs at a higher level of aggregation than the elementary aggregates in all UK price indices and therefore in addition to the RPI price bounce is a feature of CPI and CPIH which the article neglects to mention. 


    Much of the questionable inference in the article appears to be derived from a misinterpretation of the short quote taken from "The United Nations Practical Guide to Producing Consumer Price Indices" –


    "A key result is that the Carli formula for the arithmetic average of price relatives has an upward bias relative to the trend in average item prices. In particular the Carli suffers from lack of transitivity i.e. when prices return to an earlier level the chained index doesn't. Consequently, it is a formula to be avoided and some judge that it should be prohibited."


    The opening sentence of the forward of the UN guide starts with –


    "This Handbook is targeted at developing countries…"


    This raises the question of why ONS chose this particular methodological source.  There are other international sources at Eurostat and the ILO that are more appropriate to a developed country like the UK.  They offer a different set of conclusions that the article neglects to mention.


    Quoting the UN guide the article refers to Carli having an "upward bias relative to the trend in average item prices".  Quite what that means is not clear but on a reasonable interpretation the chart below from a SUN post of October 2014 based on analysis from the Johnson Review shows that for vacuum cleaners this statement does not hold.  For this Johnson derived analysis the RPI type item index is an annual chain linked Carli unlike in the RPI methodology where Carli is only used as a direct index.  However the chart shows that the UN guide statement does not even hold when the guide would expect the item index trend to be biased upwards by price bounce.




    The differences in the above chart between the RPI or CPI indices and the average price index are conventionally used as an indicator of implied quality change.  The Johnson Review used such differences as measures of implied quality change and commented that implied quality change can have a major influence on the indices.  There were changes in the treatment of non-comparable substitutions/implied quality change in 2010 for clothing.   This is likely to have resulted in a different relationship for clothing from that for vacuum cleaners shown in the above chart.  The article's case against Carli places considerable importance on the behaviour of clothing since 2010 but neglects to mention this significant change in methodology.


    The article is dismissive of expert contributions such as that from Mark Courtney without directly addressing the arguments.  There is an associated issue here with how reliably the advice ONS receives from its advisory panels is reported as the recent SUN posts on chain linking illustrate.  The article neglects to mention contributions on SUN even though recent postings would have provided the information to avoid the error on the RPI, Carli and transitivity/price bounce.


    The recently published Code of Practice for Statistics v2 offers a regulatory perspective on the article. 


    The code includes the Quality principle Q2.1 –


    Methods and processes should be based on national or international good practice, scientific principles, or established professional consensus.


    The quality of the section of the article on the formula effect measured against Q2.1 would arguably fail all its requirements.


    There appears to be a strong argument that unless improved this article would fail to meet the requirements of the Trustworthiness Pillar of the Code of Practice and the standards of behaviour set out in the Civil Service Code.


    An explanation from ONS, perhaps?


    All the best.




    The ONS article "Shortcomings of the Retail Prices Index as a measure of inflation" can be found at – https://www.ons.gov.uk/economy/inflationandpriceindices/articles/shortcomingsoftheretailpricesindexasameasureofinflation/2018-03-08/pdf

  • 9.  RE: The debate over the Retail Prices Index

    Posted 12-03-2018 02:16

    Dear Arthur: 

    Thank you for your very interesting note.

    I added a document to the library with my own critique on the shortcomings paper.

    I didn't say anything about the discussion of the formula effect as I was more comfortable with the switch from RPI to RPIJ than you were.  Still, it seemed to me the document created a misleading impression about international rejection of the Carli formula. While it was true that it was pretty much expunged from the Canadian CPI in 1978, it was and probably still is much used in Canadian producer price indices in the context of pps sampling. If pps samples were used more in the Canadian CPI (they were virtually non-existent there in 1978 and long after) the Carli formula might have been used a little more.

    Best regards,



  • 10.  RE: The debate over the Retail Prices Index

    Posted 12-03-2018 22:59



    Thank you for your response and the very helpful document that you added to library.


    I purposely confined my comments to the formula effect section and left the other sections to those like you who are better able to comment.


    In general my concerns with the article are twofold.


    My primary concern is less with the RPI/RPIJ than the potential implications of the article being used by ONS to restrict the methodologies available for use by the HCI.  As one example, Carli should be available to use if the empirical evidence for particular products/services or the index as a whole indicates that it is an appropriate formula to use.   This does not mean that the use of Carli should match its use in the RPI or any such arbitrary target.  There are also additional complexities with other issues that interact with the choice of formula like quality adjustment and these may well be more important in the construction of the HCI.


    The secondary concern which is related to the primary concern is whether the approach adopted in the article is appropriate.  There appears to be the potential for issues with the codes under which ONS operates.


    There is though one technical statistical point that your document reminded me of that I had missed.  This is the index used by ONS for rental equivalence.


    First a question for ONS – has the methodology article for the rental equivalence index (IPHRP) been published?


    This is important given the apparent 9 month or so lag inherent in the index and the implications that has for what the index actually measures.  There is also an issue given the administrative source of how stable over time the index will be in what it measures.  This is more important from a household perspective than a macroeconomic perspective because macroeconomists have the tools to cope with such uncertainties but the general public does not.  This highlights the issue of whether rental equivalence as implemented by ONS can be considered appropriate for a household index.


    All the best.



  • 11.  RE: The debate over the Retail Prices Index

    Posted 14-03-2018 20:44

    The discussion so far has already exposed the errors in the way the ONS paper, "Shortcomings of the Retail Prices Index as a measure of inflation," deals with the formula effect and how the coverage issues it highlights actually make the RPI look rather better than its favoured CPIH.  A third feature of the paper is the very selective way it deals with clothing inflation, claiming that the current clothing inflation figures show that in practice (the ONS has conceded that there is no general theoretical superiority) the Jevons elementary aggregation formula is always the most appropriate.  It is common ground that since 2010 the CPI clothing index has been more plausible than the RPI clothing index, just as before 2010 the RPI clothing index was more plausible than the CPI clothing index.  That is because, prior to 2010, we had a huge negative sampling error for clothing, and the formula effect wedge tended to offset it in the case of the RPI and exaggerate it in the case of the CPI; whereas, post-2010 we have a huge positive sampling error for clothing, and the even larger formula effect wedge tends to offset it for the CPI and exaggerate it for the RPI.  Without being able to disentangle the formula effect from the sampling error, one cannot draw any conclusions about the performance of the aggregation formulae.

    I've placed in the Library a paper "UK Clothing Inflation 1997-2016" (also available at ssrn.com/abstract=3140666) which examines this question in some detail.  As it happens, we can use movements in the implied relative clothing volumes and the results of the ONS' 2011/12 clothing price pilot, to come up with a fair estimate of the effects of the excessively loose clothing price sampling post-2010.  This shows that, with an undistorted clothing price sample, there would be much reduced formula effect wedge and that - consistent with results in other sectors - the overestimation of a target Fisher index by the RPI would be about equal to the underestimation by the CPI.  And this is not a mere curiosity.  By building on the 2011/12 clothing price pilot the ONS could, if it wished, improve the methodology for clothing price sampling to greatly reduce the formula effect wedge and improve the accuracy of both the RPI and CPI clothing indices.

    Mark Courtney

  • 12.  RE: The debate over the Retail Prices Index

    Posted 15-03-2018 12:01

    One other issue with this ONS article is the timing of its publication – this seems rather odd and warrants explanation from ONS. 


    There would appear to be no obvious reason to rush the publication of the article and circumvent the usual arrangements of advisory panel meetings for the governance of consumer price indices.


    The article in draft or final form did not appear on the agenda of the January meeting of the Technical Panel or the February meeting of the Stakeholder Panel although the article was published a relatively short time afterwards at the beginning of March.   The timetable for publication appears rushed and arguably the article appears so too.


    The assumption must be that there is nothing untoward here just something akin to an accidental and unexpected juxtaposition of events to explain the timing of the publication that ONS can provide easily and quickly.


    However beyond that there is the issue of the transparency of the governance process which is missing here – users have been left very much in the dark.


    Presumably in line with past practice the advice of members of both advisory panels was sought before the publication of such a potentially controversial article.  If this was the case then the difficulty is that this arrangement outside of meetings of the panels is not transparent.  It effectively circumvents the publication of the draft article and the meeting minutes which would contain the advice of the panels.


    • Would ONS confirm whether or not advice was sought from the members of the advisory panels and if so when and how was this done?
    • If advice was sought would ONS publish the draft of the article seen by the panels and, after seeking members' permission, publish the advice received?


    Given that the usual governance procedures don't appear to have been followed there is also the issue of whether or not prior to publication the article in final or draft form was shared with other groups and whether or not their advice or comments were sought or received.  Such other groups may include, for example, the Tripartite/Tetrapartite Group or The Economic Experts Working Group.


    • Would ONS confirm which, if any, other groups had a sight of the article in draft or final form before publication and whether or not advice/comments was sought?
    • If other groups were given sight of advance copies would ONS publish the draft of the article seen by other groups and publish any advice/comments received?


    There is a lack of transparency in the deliberations of both the Tripartite/Tetrapartite Group and The Economic Experts Working Group.   This gives rise to a question of whether the priorities of some of the members of either of these, or other, groups may have contributed to a rushed publication of this article.


    The information requested in this post relates to the governance of price indices and, for example, could be released quickly as supplementary papers for the January and February meetings of the two advisory panels.


    All the best.



  • 13.  RE: The debate over the Retail Prices Index

    Posted 15-03-2018 17:12

    Dear Mark Courtney:

    Thank you for your very interesting paper.

    If a third of clothing items in the UK consumer price sample can be considered as seasonal, as indicated on page 8 of your paper, any review of the measurement of clothing inflation should consider the options for dealing with seasonal goods. As far as I know this has never been properly done for clothing in UK consumer price indices.

    The only recent study on seasonal weighting for clothing consumer price series for any European country in recent years that I am aware of is the paper presented at the Joint UNECE/ILO Meeting on Consumer Price Indices 10 – 12 May 2010, Palais des Nations, Geneva by Monica Montella and Franco Mostacci:  "The impact of European Commission Regulation on the treatment of seasonality in the HICP for Italian clothing". Unfortunately, its authors were stymied by the very rigid restrictions on seasonal weighting imposed by the EC regulation on seasonal goods, and Istat did not decide to go with seasonal weighting for clothing in the Italian HICP.

    The EC regulation does not, of course, apply to the RPI nor to the CPI if it were no longer defined to be identical with the UK HICP. More promising seasonal weighting alternatives could be envisioned, based on the Rothwell or Balk formulas.

    In my view, linking at the year for consumer price series should be considered as an alternative to linking at December or January, which has obvious advantages when dealing with seasonal goods.

    The quality adjustment problems you mention are more serious for seasonal items than for non-seasonal items.

    Best regards,


  • 14.  RE: The debate over the Retail Prices Index

    Posted 17-03-2018 13:13
    Assuming constant relative volumes for Clothing compared with other items, the correct inflation index would be about half way between the RPI and CPI estimates.

    Next week we will have another year's figures for weights etc, which will add knowledge to this situation.


  • 15.  RE: The debate over the Retail Prices Index

    Posted 17-06-2018 21:27



    A few technical questions concerning the following chart from the March article "Shortcomings of the Retail Prices Index as a measure of inflation" which I understand the National Statistician included in his June 13th PowerPoint presentation.


    Figure 2: A comparison of price index and average price change for items of clothing, using the Carli and Jevons formulae, January 2010 to January 2018

    I will admit that looking at the chart more closely and reading the article text does not make interpretation of the chart any clearer.  For example, it is not clear how to interpret "Each marker is for a particular clothing item within the wider clothing category", or the "expected" line.


    The "expected" line looks a little strange with the absence of any measure or indication of variability for what is described as the "average price".  The vacuum cleaner chart below shows an example of variation in average price –




    Given the issues with non-comparable substitutions in clothing its average price series would reasonably be expected to show more variation than vacuum cleaners.


    Rupert de Vincent-Humphreys in his paper for the Technical Panel – APCP-T(17)02: RPI and CPI: a tale of two formulae: https://www.statisticsauthority.gov.uk/wp-content/uploads/2017/02/APCP-T1702-RPI-and-CPI-a-tale-of-two-formulae.pdf  – has indicated that there are potential problems with calculating average prices for clothing.


    "High product turnover
    Generally cannot calculate matched observation price change over the year:
    Clothing items typically change 2-3 times a year."


    A few questions though apologies if I've got the wrong end of the stick –


    • How is the "expected" line in the chart calculated?
    • What are the error bounds for the "expected" line and how are they calculated?
    • Could ONS publish a revised version of the chart including the error bounds?
    • What does each data point on the chart for Carli and Jevons represent, does each refer to a "particular clothing item" and if so how were they selected?


    All the best.



  • 16.  RE: The debate over the Retail Prices Index

    Posted 19-06-2018 19:00
    Judging from the graph, the "expected" line appears to be the "Change in index %"="Change in average price %" line. That is, the "expected" line is the Dutot index. So the graph demonstrates that the Jevons and Dutot indices produce similar values and are generally smaller than the Carli index. This is not news.

    The reason that the Dutot index values are similar to the downwardly biased Jevons index values is that the Dutot index is also downwardly biased because there is a negative correlation between price movements and base prices. That is, the Dutot index gives heavier weight to smaller price movements.

    The clinching argument for the Jevons and Dutot indices has always been the democratic one: the Carli is outvoted 2:1. (The argument about "price bounce" is not relevant because the target weighted index does suffer from "price bounce". Indeed, one could present this as an argument in favour of the Carli index and against the Jevons and Dutot indices because the Carli index better reflects the characteristics of the target index.)

    What we need are a few more unbiased indices, so that they can out-vote the Jevons and Dutot.

    One possibility is random weights - this is no worse than arbitrary fixed weights.

    A variation on this, using fixed weights in a random order, is to modify the Dutot so that the base prices are assigned randomly to products, rather than each product using its own base price. This would remove the negative correlation problem.

    If random weights are deemed undesirable, we could apply a fixed re-ordering of base prices. For example, rank products in base price order then assign new base prices from ranks 1,3,4,5 ... 8,6,4,2. This applies the extreme base prices (large or small) to the extreme price movements. If this is not desirable, we could apply the middling base prices to the extreme price movements. Other options are possible.

    Any other suggestions?

    If we can devise enough unbiased elementary index formulae, we could vote the Jevons and Dutot out of existence.

    John Wood

    Although this note is slightly tongue-in-cheek, it has a serious purpose. Without knowledge of the true weights for the elementary aggregates, none of the outré index formulae I have suggested are any worse (or any better) than the standard Jevons, Dutot and Carli indices, although I, personally, would claim that they are better than the Jevons and Dutot indices because they are not biased.

  • 17.  RE: The debate over the Retail Prices Index

    Posted 20-06-2018 16:22



    I did wonder if the "expected" line was based on a Dutot index but then why wouldn't James have said so in his article.


    ONS have different average price calculations as can be seen from another version of the ONS vacuum cleaners chart.  This version also includes Dutot which I usually leave out because it is so close to Carli that it confuses things.


    I'm sure that ONS will provide an explanation of their clothing chart in the fullness of time.


    All the best.



  • 18.  RE: The debate over the Retail Prices Index

    Posted 03-07-2018 17:21

    Dear Arthur,

    Thanks for your query. The data points on the chart correspond to specific items of clothing (e.g. men's jeans). For each of these clothing items, we calculated the change in the average price over the period, and plotted this against the change in the index using Jevons and Carli separately. For example, the 2 data points with just over 50% increase in average price (one for Carli and one for Jevons) are both for the same item of clothing (therefore both showing the same increase in average price), but the increase in the index over the period is much higher using the Carli formula.

    The 'expected' line in the chart does not have underlying data; as John says it illustrates what a 1:1 relationship between % change in the average price and % change in the index would look like over the period (i.e. the line is y=x) . In a sense this is similar to Dutot, but does not have the reliance on matched pairs over the period. This was included to provide a point of reference to compare the results using Carli and Jevons; all else being equal (notwithstanding sample changes etc), one would expect a 50% increase in average price of an item of clothing over the period to equate to a 50% increase in the index for that item.

    I hope this clarifies,


  • 19.  RE: The debate over the Retail Prices Index

    Posted 04-07-2018 12:34



    Thank you for the explanation of the chart.


    I don't think that the data for the chart was released when the article was published in March.  If I'm right could you let me have the data or post it on SUN please?


    From what you say the chart appears to be based on matched data for the different items of clothing so it would be useful to look at the chart in terms of the matched data.


    I agree that the "expected" line as a ratio of two averages is a little like a Dutot index though the ratio is not comparing like with like.


    It needs more thought but the assumption that "one would expect a 50% increase in average price of an item of clothing over the period to equate to a 50% increase in the index for that item" may not be in line with the constant quality assumption that underlies both the RPI and CPI.  It would appear to depend on how the average price is calculated so a couple of additional questions. 


    How are the average prices calculated for the chart?


    How are non-comparable products treated in the calculation of the average prices?


    All the best.



  • 20.  RE: The debate over the Retail Prices Index

    Posted 06-07-2018 15:39
    Dear Arthur,

    The data were published shortly after on request

    On your other questions, I'm afraid I will need to come back to these when I return from leave in a week's time.



  • 21.  RE: The debate over the Retail Prices Index

    Posted 26-07-2018 10:35

    Hi Arthur,

    Sorry for the delay in responding. I've answered your questions below:

    As mentioned in my previous post, we published the data underlying the chart shortly after the publication.


    The average price is the arithmetic mean of prices for that item in the period in question, so treatment of non-comparables isn't relevant in this context.


    As you say, the sentence "one would expect a 50% increase in average price of an item of clothing over the period to equate to a 50% increase in the index for that item" is an assumption. It is caveated in the ensuing sentences, "We would expect some variation, however, due to chain-linking and the formula used. In addition, changes to the sample would also show up as deviations from the expected line."


    With these points in mind, I think it is important not to overinterpret the chart. There are some assumptions involved, but it serves to highlight the often implausible changes in the index when the Carli formula is used, in comparison to the Jevons formula.

    I hope this helps,


  • 22.  RE: The debate over the Retail Prices Index

    Posted 18-09-2018 14:00


    We have looked into whether we can produce Dutot estimates to accompany the Jevons and Carli estimates in Figure 2 of the Shortcomings of the RPI paper. Unfortunately, however, these are not readily available and would take some time to produce. They could be produced as a chargeable request. Alternatively, it is likely that, in the longer term, we will need to produce Dutot indices as part of the work to review the criteria for applying elementary aggregate formula, under item 3.2.6 of our Consumer Prices Development Plan, so could provide estimates then.

    Kind regards,


  • 23.  RE: The debate over the Retail Prices Index

    Posted 26-09-2018 14:23
      |   view attached



    Thank you for your response.


    First a quick explanation why I think that the Dutot indices are important – I am just giving my view and not looking for an official response. 


    This all relates to the House of Lords Committee investigation into the RPI and it is to be hoped that the Dutot indices can be provided before the Committee concludes its investigation.  ONS did provide a Dutot index to the Johnson Review for one clothing item and so the coding has been done previously but I'll return to this below. 


    First though I will set out why I believe clothing Dutot indices are important.


    The HoL Committee has taken evidence including from the National Statistician that there is a problem with the change in clothing data collection methodology from 2010.  Key elements of the 2010 methodology change include switching off in large part implicit quality adjustment and including discounted January sales prices.  Arguably these changes mean that clothing indices no longer meet the constant quality requirement of RPI or CPI but that is for another time.  The immediate issue is that Carli is unlikely to be an appropriate formula to use with such a methodology which leads to the question of which formula would be appropriate.


    The chart in the March article presents Jevons as an alternative formula but the hypothesis implicit in the chart is that change in average price is the prime determinant of an appropriate formula – Dutot is, of course, a change in average prices as John Wood pointed out back in June.  Under this assumption Dutot would therefore be likely to provide a "better" formula than Jevons for clothing conceptually and probably in practice. 


    Dutot is also a standard methodology in the RPI so its use for clothing arguably would not represent a major methodological change.   Therefore one possible option for improving the RPI rather than changing the collection methodology again may be to replace Carli with Dutot for clothing.


    The difficulty is, of course, that ONS do not publish Dutot indices for clothing to test the hypothesis.  I was waiting for the Dutot indices to be calculated by ONS before I put the hypothesis to the HoL Committee


    If the Dutot indices are unlikely to appear before the Committee investigation ends as your post suggests then this creates a problem. 


    However there is a first approximation to the change in the Dutot indices in the March chart's "expected" value.  There are potentially significant issues with this but it is available as an ONS calculation.  The expected value would appear to be derived from a direct Dutot index with January 2010 as its base and no chain linking.  Dutot indices in the RPI and CPI are, of course, annual direct indices that are chain linked at a higher level in the overall index calculation.


    I've added the "expected" value to the chart – see below.  The individual clothing item expected values follow the expected line very closely, if not exactly, as would be expected. What is required are the chain linked annual direct elementary aggregate Dutot indices to compare with the Carli and Jevons data in the chart.  It would seem likely that such a Dutot index would provide a fit at least comparable to Jevons.


    Your post says that clothing Dutot indices are not readily available and would take some time to produce but a Dutot index was calculated for clothing item "T-shirts" for the Johnson Review.  It was part of Annex B of the report on implicit quality adjustment.


    This implies that ONS already have code etc to calculate Dutot indices for clothing and the requirement for a chargeable request would seem excessive.


    I attach the relevant worksheet from the published spreadsheet of Johnson Review supplementary data.  The data included in the worksheet is a series from January 1996 to December 2013 of average prices, and a direct and a chain linked Dutot index.   Extending the series to January 2018 should not be difficult.


    Interestingly from the worksheet the change in the average price for T-shirts and the chained Dutot index between January 2010 and December 2013 are very similar at respectively 1.58 and 1.55. 


    All the best.




  • 24.  RE: The debate over the Retail Prices Index

    Posted 03-10-2018 20:14


    Unfortunately the Johnson Review code would not allow us to produce the Dutot indices more quickly. The time consuming part of the task would be the extraction and processing of historical data, since the live production system only holds 13 months of rolling data. The Dutot calculation itself is relatively straightforward.

    As indicated in my previous message, we are happy to produce this data as part of a chargeable request.

    Kind regards,


  • 25.  RE: The debate over the Retail Prices Index

    Posted 07-10-2018 11:42



    Thank you for your post.


    The post doesn't directly address the issue of the code that was used for the Johnson Review to extract and process its data only the calculation of the Dutot index.


    First the Johnson analysis was over 17 years whereas the March article analysis was only over 8 years.   This implies that the former extracted and processed over twice as many months of data per item as the maximum that would be required for the latter.


    I recognise that extracting and processing the data is the more time consuming process and the Johnson analysis 200+ months of data is unlikely to have been extracted by hand but automated. Once that code is available for one item then presumably extracting the data for different items should require little more than the item identifier to be changed.


    The Johnson analysis required every month's data to be extracted which is not necessarily the case for the March article – the Dutot index required is the single January 2010 to January 2018 comparison. You have confirmed that after the change of methodology in 2010 there would be no imputed base data and hence the base month data doesn't change during the year only after chain linking. Arguably therefore to obtain the Dutot index change between January 2010 and January 2018 would only require the average price for the months around the chain linking in each intervening year. This would probably mean only average prices from about a quarter of the twelve/thirteen months would be required.


    This would imply that only about one eighth of the Johnson analysis data per item would be required to be extracted.


    However there would be real value in having the average prices and Dutot indices for all the months of each year to check the validity of the choice of January for the comparison between 2010 and 2018. For example, January is a sale month which could adversely affect the comparison. Testing the comparison for different months may offer different results and possibly different conclusions but that is for another time.


    Arguably though, the issue is less about the technical minutiae of data extraction than an apparent reluctance on the part of ONS to follow up on the wider implications of Figure 2 in the March paper – failing to look beyond Jevons and Carli could be interpreted as an example of the False Dilemma logical fallacy where two alternative statements are held to be the only possible options when in reality there are more.


    All the best.



  • 26.  RE: The debate over the Retail Prices Index

    Posted 12-10-2018 10:33


    The process for extracting and processing historical data is largely manual. For the Johnson Review, code was only written to calculate price indices from a pre-prepared dataset. Therefore there is nothing we can use to speed up this task.

    As indicated in my earlier post, in the future we plan to look at the criteria for applying elementary aggregate formulae and intend to consider Dutot indices as part of this work. The chart in Shortcomings of the RPI was provided simply for illustrative purposes, to highlight the issues with the Carli clothing index.

    Kind regards,


  • 27.  RE: The debate over the Retail Prices Index

    Posted 14-10-2018 20:45



    Thank you for your post.


    The confirmation that Dutot will be considered as part of future work on the elementary aggregate formulae is very welcome.


    The point about the March chart being for purely illustrative purposes is also welcome. Given the changes that were made to clothing data collection in 2010 the effect on Carli is unsurprising given the known issues with certain types of heterogeneity. The relaxation of the constant quality requirement for clothing and the inclusion of January sale prices was almost certain to create problems. To help overcome these problems the issue is whether to change the collection methodology again or change the formula. As an advocate of a less rigid approach to the constant quality convention I wouldn't automatically favour changing the former in favour of maintaining the use of Carli – prior to 2010 all the formulae probably underestimated clothing inflation so the pre-2010 methodology is unlikely to offer a solution.


    The evidence is still not there to decide which path to take with clothing. That will require amongst other things additional historic analysis so it is unfortunate that the Johnson Review didn't put in place automated systems to generate the historic data quickly and perhaps more importantly reliably. This places another question mark over the quality of the Johnson analysis though too much time has passed to take that particular issue any further.


    All the best.



  • 28.  RE: The debate over the Retail Prices Index

    Posted 20-03-2018 11:34
    Hi All

    The Bank of England has responded to my email about inflation measurement with a fascinating albeit selective and flawed reply. However we do have at least a view on what it thinks about inflation measurement which I think should be welcomed as a development as it rarely does so. Here it is.

    Dear Mr Richards

    Thank you for your letter, addressed to the Governor, of 20 February regarding the Retail Prices Index (RPI). 


    Although many of the matters you raise are primarily for HMT and the ONS to address, the Bank of England has a clear interest in the accurate measurement of inflation and informed public understanding of what those measures represent. 


    The Bank's understanding is that members of the Royal Statistical Society (RSS) have made their views plain to ONS and, for instance, have worked closely together with ONS on the development of the experimental Household Cost Indices. Members of Bank staff regularly engage with the RSS, ONS and others via our involvement in the ONS's technical and stakeholder panels on consumer price statistics. That seems to us the appropriate, and most inclusive, forum for such engagement, given the wide variety of interests involved in the development of consumer price statistics.


    As you are probably aware, following a detailed review, the National Statistician and the UK Statistics Authority concluded that the methods used to produce the RPI were not consistent with internationally recognised best practices.  The RPI subsequently lost its status as a National Statistic, and ONS has taken further steps to discourage its continued use.  For example, it has recently released an article on the shortcomings of the RPI. The Bank agrees with that assessment. You can read this article here:




    No measure of consumer prices is perfect. We agree that the single biggest shortcoming of the current CPI is that it excludes the consumption price of owner-occupied housing.  As you will know, measuring this is not straightforward because the consumption cost of owner-occupied housing services is not directly observable. As you note, people do not pay rent to themselves to live in their own home. After a detailed review of both principles and practicalities, ONS opted to incorporate owner-occupied housing via the rental-equivalence approach. This is considered an economically sound concept and it is easy to understand, the price a homeowner would have to pay to rent a home similar to their own, but it is clearly an imputed one. 


    As you suggest, the other main alternative is the net acquisitions approach. Rental-equivalence was favoured by ONS for the reasons set out (here). In our view, this judgement seems both reasonable and practically compelling given data limitations.  In any event, an important factor in any measure of consumer prices is avoiding the influence of movements in asset price valuations (such as land prices and asset valuations of housing structures).  RPI suffers from this problem.  Indeed, by the inclusion of mortgage interest payments, RPI conflates the consumption cost of housing not only with asset valuations, but also with the costs of financing the acquisition of those assets.


    We should stress that none of this is to say that house prices and mortgage interest payments do not matter. Accurate information on these is central to much of the work of the Bank's Monetary Policy and Financial Policy Committees as well as many other economic and financial policymakers.  They matter a great deal, and although they do not belong in a measure of the cost of consumption, it is important that these are accurately measured in and of themselves so that different users can make use of a full range of statistics as appropriate for their own needs.


    Regarding the Governor's appearance at the House of Lords Select Committee on Economic Affairs session on 30 January, the official transcript can be found at http://data.parliament.uk/writtenevidence/committeeevidence.svc/evidencedocument/economic-affairs-committee/governor-of-the-bank-of-england-2017/oral/77776.html.


    I thank you again for your letter.


    Kind regards

    You will have your own views on this but I have posted an initial response on Notayesmanseconomics today and a link to it is below as this is already a long item. Two main points are that we need a new way ahead and I note that my opponents seem to be weakening.

    It is time to replace consumer inflation measures with inflation faced by us

    Notayesmanseconomics's Blog remove preview
    It is time to replace consumer inflation measures with inflation faced by us
    Let me open today by agreeing with the Bank of England. As many of you are aware I wrote to Governor Carney challenging the testimony he gave to the House of Lords on the 30th of January. Here is p...
    View this on Notayesmanseconomics's Blog >


    Shaun Richards


  • 29.  RE: The debate over the Retail Prices Index

    Posted 21-03-2018 12:26

    Dear Shaun:

    Everyone in the RPI CPI User Group should be grateful to you for taking the trouble to write to Governor Carney on his views on inflation measures and posting the response he received.

    Unfortunately it seems the Bank of England's understanding of these measures is quite shallow. It makes no sense to criticize the accounting approach to owner-occupied housing used in the RPI because it includes a mortgage interest component if one's favoured alternative is imputed rents. A landlord has to charge a rent that covers their own mortgage interest costs, and that means all mortgage interest costs for dwelling and serviced lot.

    The letter bypasses the glaring inconsistency between Governor Carney's trashing  the approach to OOH in the RPI in his testimony before a committee of the House of Lords and his support for the same approach in the Canadian CPI during his years at the Bank of Canada and at the Department of Finance.

    Unlike the Governor of the Bank of England, who must follow a remit from the Chancellor of the Exchequer, the Governor of the Bank of Canada negotiates the target inflation indicator, the target rate and so forth with the Minister of Finance. Nevertheless, in November 2011, when it was not only his right but his duty to try to replace or modify the target inflation indicator, the Canadian CPI, because of its treatment of OOH, he declined to do so.

    Since it seems no explanation will ever come from Governor Carney himself I will repeat my own conclusion. Governor Carney never favoured the accounting approach.  Based on the 2015 Bank of Canada paper by Patrick Sabourin and Pierre Duguay, both of whom served under him when he was Governor, I suspect he favoured at that time either  a rental equivalence or opportunity cost approach to OOH for the target inflation indicator. Although the two approaches can give dramatically different results empirically, they are ideologically similar. Both are use-for-consumption approaches pur et dur.

    Rather than trying to change the target inflation indicator with the 2011 renewal agreement, Governor Carney simply sought to reduce the constraints a measure he had little respect for imposed on him. "Inflation targeting" in previous renewal agreements was replaced with "flexible inflation targeting", with strong emphasis on the word added.

    Does Governor Carney have any greater respect for the CPI or the CPIH? Not much, I would think. If one takes him at his word in his New York City speech, "A Monetary Policy Framework for All Seasons", he favours the central bank using a national approach, like the RPI or the HCIs, rather than a domestic approach, like the CPI or CPIH, in measuring inflation. The House of Commons Treasury Committee should have asked him about this in February 2013, when they were tasked with assessing his suitability to be central bank governor, but they didn't bother.

    Thank you again for providing us with the reply you received from the Bank of England.

    Best regards,


  • 30.  RE: The debate over the Retail Prices Index

    Posted 29-03-2018 14:09
    Dear all,

    Thanks for your comments on the recent RPI article, and sorry for the delay in responding. I've tried to address all your questions below, but if there's anything I've missed please do let me know.


    Communication with Advisory Panels and other groups, and the timing of publication

    A draft was shared by correspondence with the Advisory Panels, and it was also taken to the Economic Experts Working Group. Just to clarify, we do not publish drafts of documents. There was no specific reason for the timing of this publication. We considered it important to present a synthesis of the issues affecting the RPI, and published it as soon as we had completed the work.


    Carli (including price bounce and chain drift)

    The Johnson review set out that the chain drift was affected by the interaction between the higher level Lowe indices and the elementary indices:


    "In practice, price indices are linked at higher levels of aggregation. It is the interaction between the higher level formula (a weighted arithmetic average called a Lowe index) and the unweighted average that causes chain drift."


    In this article we were striving for a straightforward example of the transitivity issue to communicate to users with a wide range of expertise, hence the choice for Annex A. This point shouldn't distract from the main message of the article, which is that the weight of opinion is against the Carli and it is not regarded as international best practice. Whilst it is not expressly prohibited in the HICP, it is certainly discouraged:


    "When compiling price indices for elementary aggregates either the ratio of arithmetic mean prices or the ratio of geometric mean prices shall be used. An alternative formula may be used provided that it fulfils the comparability requirement laid down in Article 7. 2. The arithmetic mean of price relatives should not normally be used, as it will in many circumstances result in failure to meet the comparability requirement. It may be used exceptionally where it can be shown not to fail the comparability requirement."

    I hope this helps,


  • 31.  RE: The debate over the Retail Prices Index

    Posted 07-04-2018 16:53



    Just a couple of comments.


    Communication with Advisory Panels and other groups, and the timing of publication

    There appears to be a hint of contradiction in the final two sentences in this section –


    "There was no specific reason for the timing of this publication". 
    "We considered it important to present a synthesis of the issues affecting the RPI, and published it as soon as we had completed the work"


    In contrast to the first of the above sentences the second would suggest that there was a specific reason for the timing of the article. That reason would appear to be related to the unstated reasons why at that particular time ONS considered it important to present a synthesis of the issues.


    Those unstated reasons appear to have had sufficient importance and urgency to result in a decision not to wait for the next advisory panel meetings with their albeit limited transparency.


    Carli (including price bounce and chain drift)

    This section quotes two sentences from a short paragraph from page 142 of the Johnson Review.


    Adding the final third sentence of the paragraph, for example, provides a fuller picture.  Below is the paragraph – retaining the italicised sentences from your post –


    "In practice, price indices are linked at higher levels of aggregation (see Chapter 2 for details). It is the interaction between the higher level formula (a weighted arithmetic average called a Lowe index) and the unweighted average that causes chain drift. This interaction effect between the Lowe and the unweighted average means that indices using Jevons and Dutot at the elementary aggregate level will also exhibit some chain drift."


    To finish, links with the text to the HICP regulations and ILO manual can be found at the SUN post below.  The former are arguably less relevant than the latter for a household index used for domestic policy and commercial purposes like the RPI.  The HICP in contrast is a macroeconomic index specifically designed for international comparisons.  It is important that even for such a different context EU regulations do not preclude the use of Carli.


    The evidence to support the ONS opinion that the use of Carli within the RPI is not consistent with international standards would appear to be at best tenuous.


    All the best.




    SUN post – http://www.statsusernet.org.uk/communities/community-home/digestviewer/viewthread?MessageKey=9eb32e6c-01f1-4b8f-9e3a-02194dc90390&CommunityKey=3fb113ec-7c7f-424c-aad9-ae72f0a40f65&tab=digestviewer#bm9eb32e6c-01f1-4b8f-9e3a-02194dc90390

  • 32.  RE: The debate over the Retail Prices Index

    Posted 15-04-2018 16:03

    Some UG members may have seen the article "The rise and rise of inflation" in the April 2018 edition of the RSS Significance magazine. The article is an introduction to the book by the same authors "Inflation: History and Measurement" which can be expected to make an interesting read.


    The authors of the book and the Significance article have close links to ONS – see, for example, https://blog.ons.gov.uk/2017/11/24/the-inflation-story-history-of-prices-measurement-told-for-the-first-time-in-new-book/


    The Significance article for the most part provides a historical perspective which can be compared with recent ONS publications to illustrate how, among other things, the ONS position on the use of Carli in the RPI appears to have changed.


    For example, the Significance article includes a timely reminder of the recommendation about the use of Carli within the RPI made by Professor Erwin Diewert in his paper "Consumer Price Statistics in the UK".  This paper was commissioned by ONS as part of the evidence leading up to the de-designation of the RPI.   


    The recommendation as set out in the paper's abstract is as follows –


     "The most important recommendation for improvement is (i) The Retail Price Index (RPI) should drop its use of the Carli index as an elementary index…"


    The Significance article does not provide a reference to Professor Diewert's paper* nor provide the reason why he came to his recommendation.  That reason appears to be related to Carli failing a variant of the "time reversal" test.


    In contrast the recent ONS article "Shortcomings of the Retail Prices Index as a measure of inflation" does not appear to mention either Professor Diewert or the time reversal test. 


    Issues such as this apparent abandonment of Professor Diewert's evidence make it difficult to have much confidence in the ongoing ONS critique of the use of Carli within the RPI or any future index such as the HCI.


    All the best.