I have received a very helpful short email from Chris Payne who is a member of the Technical Panel's secretariat. The email provides more information about the Panel's deliberations on chain linking – the substantive paragraph from the email is at the end of the post.

The extracts from the email highlighted below in italics would suggest that there is a strong argument for revising the relevant section of the minutes to the September meeting of the Technical Panel to reflect more precisely the Panel's thinking. The Panel minutes for September were revised in February 2018 so there is a precedent for the Panel Chair to make such a revision.

The email states that the Panel –

"… *agreed that there was no theoretical reason that the current chain linking algorithm is the only approach*".

This implies agreement that it is possible to modify the chain linking algorithm to provide the desirable properties from a range of elementary aggregate formulae including all three that are currently used in the UK – Carli, Jevons and Dutot.

Professor Balk's paper shows that problems with chain linking occur at a different level in an index calculation than the elementary aggregates and again the chain linking algorithm could be modified to provide the overall index with the desired properties without the need to change the averaging functions.

However the current chain linking algorithm does have advantages. It is simple and fits easily into the no revisions convention. The existence of a theoretical anomaly does not of itself require a change to the chain linking algorithm unless it would make a practical difference to the calculation of an index. And indeed the email goes on to state that –

"*None of the panel thought that this was a fundamental issue with our price indices*…"

ONS price indices include the RPI with its reliance on Carli. Therefore one interpretation of this statement is that the Panel's view is that the current chain linking algorithm would be likely to represent sufficiently good an approximation for use with the RPI and there is no fundamentally different issue with chain drift for that index.

However, even in the absence in practice of any significant chain drift there remains the need to identify the other sources of variation that drive the formula effect between the RPI and CPI.

Work on the formula effect is particularly important and in need of being given higher priority by ONS as it is a key factor in the choice of elementary aggregate formulae in a household index like the HCI.

All the best.

Arthur

**Extract from the Technical Panel Secretariat email, Thursday 8**^{th} February 2018

The September APCP-T minutes covered the points from the AOB discussion, so I'm afraid I can't add much in the way of a fuller explanation. To clarify, they agreed that there was no theoretical reason that the current chain linking algorithm is the only approach, and they suggested that Bert Balk's paper, which we have shared with you, should answer your questions. None of the panel thought that this was a fundamental issue with our price indices, and so Nick^{*} has decided not to pursue the matter further with the panels.

^{*}Nick Vaughan Chair of Technical Panel.

Original Message:

Sent: 22-01-2018 10:21

From: Arthur Barnett

Subject: Chain linking – ONS, the Technical Panel and CPI and CPIH

Through 2017 I was engaged in a rather one sided and unproductive conversation with the Technical Panel about chain linking algorithms. The panel secretariat did, however, share an unpublished paper by Professor Bert Balk which proved very interesting. The paper indicated that the HICP is also subject to problems of chain drift (price bounce) similarly to the RPI. CPI uses HICP methodology but unlike that index and the RPI it is not linked once a year but twice. This would imply that potentially chain linking may be more of a problem for CPI and CPIH.

Bear with me while I recount the conversation with the Technical Panel about chain linking algorithms which serendipitously revealed Professor Balk's paper and the potential issue with the CPI. In two short notes to the panel for the May and September meetings I raised two questions –

*First note question –"Is there a theoretical basis which implies that the current chain linking algorithm is the only one that can be used?"*

* *

*Second note question – "What is the likely scale of the effect of using the current chain linking algorithm (CCLA) on existing UK price indices?"*

The answer I received in the minutes to the September meeting was –

*"Prof. Balk's draft paper on mixed-form indices should address this question somewhat and has been shared with Mr. Barnett. The panel thought this was sufficient to answer the question posed."*

Professor Balk's draft paper was not published alongside the minutes of the September meeting – he has since agreed to his paper being placed on SUN, see note below – which made it difficult for UG members and others to assess the statement in the minutes. However the language – "somewhat" and "sufficient" – does not suggest much precision of thinking has gone into answering the two questions. My reading of Professor Balk's paper is that it does not directly address either question. I submitted a further note to ONS asking the panel to expand on the minutes but this note was not accepted for inclusion on the agenda by the panel chair.

The paper is particularly interesting as it looks at chain linking where it actually occurs in the calculation of an index – in this case HICP. Chain linking is not carried out at the level of the elementary aggregates with the issues that raises in the use of Carli, Jevons or Dutot but at the level that weighting data is available.

Professor Balk describes the issue with the HICP as "… there seems to be a whiff of double-counting here." The solution offered is related to the use of logarithmic means instead of arithmetic means. Such an approach seems counterintuitive as the problem is arguably the result of the chain linking algorithm not the various averaging processes used elsewhere in the index calculations. However Professor Balk's solution offers another potentially simpler way of calculating the effect of using the current algorithm on UK price indices than changing the chain linking algorithm.

It will be interesting to see if ONS or the Technical Panel respond to the challenge implied by Professor Balk's paper to the UK CPI and CPIH with their double chain linking.

All the best.

Arthur

Note: Professor Balk's paper "Mixed-Form Indices: A Study of Their Properties" has not yet been published. It has been presented at the last Ottawa Group meeting, May 2017, and will be available at the OG website (www.ottawagroup.org) when the site has been updated.

At this stage Professor Balk would welcome any comments.