RPICPI User Group

Comments on Mark Courtney's Paper on CPI-RPI Differences: The Formula Effect

By Andrew Baldwin

November 30, 2012

These are my comments on Dr. Coutney's paper on the formula effect. Although there is much of interest in his study, I do not agree with his basic conclusion that the continued use of the Carli formula in the RPEI is defensible.

It is not true, as stated on p.5, that the average of the Laspeyres and Paasche price indexes, i.e. the arithmetic mean of those indexes,  is the Marshall-Edgeworth index. This  is, rather, the Marshall-Sidgwick index. The Marshall-Sidgwick index, unlike theMarshall-Edgeworth index, does not satisfy the time reversal property. Also, the Marshall-Sidgwick index, like the grossly overhyped Fisher index, is essentially insensitive to the relative magnitudes of the Laspeyres and Paasche baskets that define it. A Marshall-Sidgwick price index for the UK and the Falkland Islands would be as much influenced by the expenditure patterns  of Falkland Islands residents as  British residents. By contrast, an Edgeworth-Marshall (or Marshall-Edgeworth) index would essentially be an index based on British expenditures.

The author seems to accept the proposition that the choice of elementary aggregation formula should be a function of the elasticity of substitution implied by the use of the formula. For example, he says on p.13:

In this case, the Average of Relatives [Carli] gives a more accurate estimate than the Geometric Mean [Jevons]if the degree of substitutability between the products in the Item is low. Examination of Braithwait (1980) suggests - and it can be no more than a very broad indication - that the cut-off point, beyond which a switch from the average of relatives to the geometric-mean approach gives a better estimate, is a compensated own-price elasticity of about (minus) 0.63.

First, it is not clear in these circumstances, even if one accepted that elasticities of substitution should determine the choice, why one would opt for the Carli formula over the Dutot formula, since both imply inelastic demand. Second, Mr. Courtney's allegiance to elasticity type reasoning is fickle. For highly elastic products, the harmonic mean would be better than the geometric mean formula but his paper does not suggest any role for this formula.

In fact, the argument against the use of the harmonic mean formula is very similar to the argument against the use of the Carli formula. It satisfies neither transitivity nor the time reversal test. With annual linking such as is found in the RPI, downward chain drift could be considerable, leading the RPI to show much less inflation than it should.

Likewise, the Carli formula satisfies neither transitivity nor the time reversal test. With annual linking, upward chain drift could be considerable, leading the RPI to show much more inflation than it should.

Dr. Courtney provides evidence that the RPI series for women's outerwear fell much more strongly from 1996 to 2009 than the series for men's outerwear. This he takes as evidence that demand shifts were at work, and this, rather than the well-known problems with the Carli formula, accounts for the differences between the RPI and CPI clothing series. However, there are no comparable CPI series for men's and women's outerwear so one can't compare them against each other. Even supposing that the CPI aggregate for women's outerwear, if it could be constructed, showed a much stronger decline over the 1996 to 2009 period than its RPI counterpart, and the men's outwear series not so much, this would seem to be weak evidence that demand shifts were responsible. There will never be any divergence between chain Carli and chain Jevons indexes if all items show the same period-to-period price changes. This is much more likely to be the case of course, or approximately so, if all items are homogeneous. The more heterogeneous the sample, the greater the likelihood of price divergence which will make the formula effect important. There is much greater heterogeneity in women's outerwear than in men's outerwear. (Generally, men don't wear mink coats.) Therefore, it would hardly be surprising that the formula effect for women's outerwear would be stronger than for men's outerwear. There is no need to invoke demand shifts.

Separate empirical studies by Szulc based on Canadian data and Woolford based on Australian data have shown just how much the Carli estimates will tend to exceed corresponding Jevons estimates in virtually all cases. To ascribe these differences to demand shifts hardly seems credible. Mr. Woolford's study related to fruits and vegetables, not the categories where one would expect to see important shifts towards expensive goods.

It seems that the root of contention for a lot of people, and perhaps for Dr. Courtney as well, isn't so much what is the best formula for elementary aggregates, but whether the CPIs for clothing properly reflect the change in consumer clothing prices or are downward biased. Of course they could well be downward biased, due to quality adjustment problems, treatment of special prices, sampling of items or outlets, which have nothing to do with the choice of aggregation formula. Perhaps these should be the focus of an investigation by the RPI CPI User Group in the future.

The quality adjustment issue especially would seem to be worthy of investigation. A study based on Canadian consumer price data by Bohdan Szulc indicated that Canadian quality adjustment procedures likely overadjusted for quality improvement, creating a substantial downward bias in measured change in clothing prices. Perhaps ONS quality adjustment procedures today are much better than their Canadian counterparts at the time of the study. Nevertheless, it should be looked into.

In short, it seems that Dr. Courtney has failed to make his case for favouring the Carli formula over the Jevons formula. One could argue that it be kept around in cases where pps sampling would dictate a Carli index;  otherwise it should be excised from the RPI.

Reference

Szulc, Bohdan (1996), "Treatment of Changes in Product Quality in Consumer Price Indexes", paper for the second meeting of the Ottawa Group on Consumer Price Indexes, Stockholm, November 15-17, 1995,version revised for January 19996.