I suspect that Anne's and Gareth's contributions both illustrate the folly of making long term decisions in times of more than usual economic upheaval and uncertainty. For example, if the current low growth continues for many years then indexation by the CPI is likely to appear advantageous if unsustainable.
I think though that the argument for an uprating index based on prices rather than incomes is an argument about filling a gap in the indicators. That argument is arguably different from the political argument of which index should be used for which purposes. Government can choose to use which index it thinks appropriate in the prevailing economic and political circumstances of the time.
An uprating index based on prices will provide another perspective on what is happening in the economy and help inform the debate on such issues as indexation - well that is my hope anyway. Arthur.
Many - long overdue - thanks to all those who have commented on my note. Starting this sort of debate is precisely what I hoped to do. In due course I will update the paper.
I would like now to pick up some of the points that have been made - and in doing so also raise one or two more questions. I must first apologise for waiting so long to do this and hope that readers will not have forgotten the argument. My original paper, along with replies from Gareth and Anne, is in the library.
1. First, an important point made to me privately is that to be comprehensive the paper would need to look at the desirable characteristics of a macroeconomic index. I accept this - any thoughts on this would be welcome. I have implicitly assumed that the HICP/CPI sets the standard for a macroeconomic index - apart, of course, from its lack of owner occupied housing. But is this right?
2. Payment vs Acquisition vs Use. My paper argued that an uprating index should normally be based on payment as this is the point at which the household budget is affected. Anne stated that payment was usually rejected as a) it is theoretically inferior to the other two concepts and b) practically impossible to implement. I am puzzled as to why payment is considered theoretically inferior? I accept Anne's point that payments by credit card would need a little thinking about (and would depend partly on the treatment of interest payments) but the practical problems seem to me minor compared with those associated with use (what "use" does one get from food thrown away because it was not eaten by its sell-by date or from the article of clothing that languishes at the back of the wardrobe because you decide after buying it that it really does not suit but you were unable to return it?). Indeed I would argue that "use" is easily a more unsatisfactory concept, both theoretically and in practice, than either acquisition or payment - I agree with Don Sellwood's arguments on this (set out under "A cpi for uprating").
3. On interest, I don't think there can be much of an argument about the service charge being included and Anne makes some useful comments here. As to whether the rest of the interest payment should be included - one can indeed argue that it is a means of financing consumption rather than consumption or one can argue that it satisfies the consumer's need to have something now rather than later. What does everyone think? I would argue that borrowing to buy is now part of life.
I don't think, though, the fact that households receive interest as well as pay it alters the argument. This is not national accounts where everything has to balance. For price indices we are only looking at one side of the equation: what households spend.
4. The issue of aggregation formulas has been touched on. My (strong) feeling is that we should use the same formulae for both sorts of index unless there is a very clear reason not to. The confusion and arguments arising from the formula effect at lower level aggregation have been serious and damaging. I can see Gareth's arguments that if there are elements in an uprating index that are erratic (such as mortgage interest payments) there could be a case for smoothing them. But this, I think, would be acceptable since it would be easily explicable to a lay person. (As a more general point I think it is desirable that as much as possible of the way a price index is compiled should be both explicable and justifiable to a lay person. It is surprising how much can be explained if you do it carefully.)
5. Housing. More than one person has suggested that I should have thought about final sales or downsizing. And not everyone is entirely happy about including something that has an investment element. So let me talk about housing - specifically owner occupied housing - a little more.
The more I have thought about this, the more I believe that the argument that because housing is part investment house prices, or variables related to them, should not be included does not hold water. I do though think that the weight accorded to house prices should be adjusted downwards to allow for certain elements associated with its investment characteristics (see below).
First, why should it be included?
a. Shelter is a necessity. One can rent or buy and an index that reflects costs to the household budget should be neutral between the two.
b. The fact that owner occupied housing is treated as investment in national accounts is irrelevant in my view. We are not dealing with national accounts but with a price index. Further, national accounting (within its well known limitations) is a comprehensive system; whether something is included as investment or consumption does not a priori alter GDP (second order effects apart). But if we exclude house purchase from our price index we are missing something of crucial importance to most household budgets.
c. Anne argued, "The whole of the present economic crisis has its origins in assumptions that house prices would always increase and so I would have grave misgivings about building this assumption into such a sensitive are as consumer price indices." I assume you did not mean to say "the whole" as distinct from "part of", Anne, but clearly housing was a significant factor. And a price index would not include an assumption but what has actually happened to prices. But I think the link between house prices and the crisis makes it more important to include them (in this case also in a macroeconomic index but I will leave that argument to others.) House prices have risen in this country primarily as we have built too few in the last 2-3 decades to match the growth in demand; speculation on the back of this has added additional froth. But the result is that it costs more for people to buy a house (and indirectly also more to rent) and this should be reflected in an uprating price index.
I could make other points but I think the substance of them was in my original note so will leave it there for now.
Let's look at the qualifications. I don't think final sales come into it. Again, in a price index we are looking only at costs - not at income or monies that accrue. Pure investment buying eg for "buy to let" is another matter. The weight accorded to housing should, in my view, be adjusted to reflect the proportion of purchases that are done for this reason.
Downsizing. Thinking about this made me realise I had made one mistake in my original note. I had argued that what I called the "housing ladder" element of house purchase - the profit a houseowner has made on his existing house which is then applied to a subsequent house purchase - should be excluded. I still believe that but in addition I think the initial capital the home owner invests, plus the repayments made under any mortgage, should also be excluded from any subsequent house purchase since they should only be counted once. When we come to downsizing then, one would not normally include those purchases at all other than if there are still ongoing mortgage costs. The consequence of this would be to reduce the weight given to house prices in an uprating index. All of this of course does require not just careful thinking but also a lot of knowledge of the housing market. I assume though that the knowledge to be found in entities such as Halifax, Nationwide, the House builders' federation and similar entities would give one a reasonable steer.
My view on using the "same aggregation formulae" for indices differs from yours and possibly Gareth's.
I am reluctant to support statistics that potentially hide uncertainty and give the impression that statistical methodology is better than it is.
The formulae conventionally used all have their problems and therefore provide one of the dimensions of the uncertainty associated with price indices.
I am a little wary to offer simple illustrative examples as they can be over interpreted but hopefully the attached spreadsheet might be useful.
The examples are simplistic and far removed from the real world but hopefully illustrate a couple of points.
What the examples do not do, and are not intended to do, is to suggest Carli is superior to Jevons or vice versa. The intention is just to offer another illustration from a layman's perspective that both produce questionable results in different circumstances.
Basically the examples I have chosen show what can happen to arithmetic and geometric means of price relatives with symmetric additive changes in prices. I would argue that a layman would reasonably consider that these symmetric changes in price to cancel each other out and that "inflation" is unchanged because the aggregate cost of the two items remains the same in both time periods.
The simplest example is the top left hand one.
In this case there are 2 items A and B each with a price of £1 at time T1. The price of A decreases by 50p and B increases by 50p at time T2. Therefore the cost of the two items remains at £2 in total at time T2 the same as at T1.
The arithmetic mean of the price relatives is 1 which indicates no price change whereas the geometric mean is 0.87 indicating a fall in price which is arguably counter intuitive.
The other two examples on the left hand side vary the price of one of the items at T1 to £2. These examples show that the two averages can both imply consistent increases or decreases in "inflation". Again I would argue that the layman would again expect no change in "inflation" with these examples.
The first 3 examples illustrate how both means can give undesirable results. (As an aside the numbers can easily be changed so that the geometric mean returns a mean price relative of 1 - change the initial value of B to 50p in the third example.)
Now it can be argued that the price changes of 50p are untypically large as they equate to things like sale prices or two for one offers. The calculations to the right show what happens when the price change is reduced. The patterns remain the same but differences reduce. By the time the price change reduces to 1p there is very little difference in practice between all the calculations of averages.
These additional calculations illustrate that although there may be theoretical problems with both methodologies they may not always represent problems in practice depending upon the data. (As a further aside not all possible simple aggregation formulae will be produce undesirable results with these examples but such formulae are likely to demonstrate problems in other circumstances.)
And finally this brings me to a more general point. One of my concerns with price index methodology is the mathematics and the way it is used. With my use of simple examples I am potentially guilty of generalising from the particular but I hope that I have made it clear that that was not my intention. In general it seems to me that proponents of different methodologies are prone to selecting particular isolated mathematical results to support their case. In their defence it may be because there is no comprehensive body of supporting mathematics to describe how different functions will behave in different circumstances, or the mathematics exists but in practice is too difficult to access.
This is not to imply that mathematics has the answers which it clearly does not because the judgement of various disciplines is likely to dominate in describing such complex phenomena. However those judgements need to be based on a sound mathematical foundation.