Another issue that arises from last week's evidence session.
Lord Turnbull as part of question 39, page 12 is reported as saying the following –
"Lord Turnbull: Chief Secretary, you downplayed the view that there was a public trust problem. There are two areas of concern that diminish public trust. One is the inherent feature of parts of the RPI where, if a price goes up in one period and goes back to the same level it was at, or down and then back to the same level it was at, it is not calculated as zero change. That is a serious statistical flaw."
In response, the Chief Secretary stated: "I agree with you about the statistical imperfections of RPI" which suggests a basic lack of understanding in the Treasury about RPI methodology.
This widely held misconception quoted by Lord Turnbull probably arises because of a misunderstanding of the mathematics of Carli which does not define an index only a method of averaging price relatives. Carli is implemented in the RPI only as a direct index and is not chain linked so does not cause the problem raised by Lord Turnbull.
To be pedantic the error is to associate the problem uniquely with the RPI. The problem that Lord Turnbull identifies can occur in all UK indices – RPI, CPI and CPIH. This is because all UK indices fail the transitivity test because they all use a Laspeyres-type formula which is another arithmetic average – see, for example, the Johnson Review page 142. Professor Balk also provides more background on this issue for the HICP and by implication the CPI in his paper "Mixed-Form Indices: A Study of Their Properties". If failure of the transitivity test proved to be a significant problem in practice then it could be resolved by changing the chain linking algorithm to one compatible with an arithmetic average.
The ONS article "Shortcomings of the Retail Prices Index as a measure of inflation" which has a forward by the National Statistician does not include the problem raised by Lord Turnbull as one of the shortcomings of the RPI. The ONS article was potentially misleading though because it failed to mention that all UK indices fail the transitivity test. Such highly selective use of evidence is not helpful in ensuring that the Committee or the Treasury have a correct understanding of RPI methodology. The article also formed the background to the National Statistician's presentation at the RSS meeting on the 13th July.
Hopefully the National Statistician will be given an opportunity to correct this misconception in his evidence to the Committee this afternoon.
All the best.