Most retired people don't spend much time worrying about the relative merits of the Carli, Dutot and Jevons indices. But perhaps they should, because this apparently abstruse mathematical question could cost them a lot of money.
This is because the Office for National Statistics is consulting on changing the way the retail price index is calculated. And the change could result in smaller increases in future pensions.
To see the issue, take a simple example. Say we have two goods, A and B. In one month, A costs 100p and B costs 60p. The next month, B’s price rises to 80p and A’s falls to 80p. What is the inflation rate?
It all depends how we measure it. To calculate inflation on the Carli and Jevons bases, we take the two price relatives: 0.8 for A and 1.33 for B. The Carli index takes the average of these, multiplies by 100 and subtracts 100. This gives us inflation of 6.6 per cent. The Jevons index multiplies the two price relatives and takes the square root, and then multiplies by 100 and subtracts 100. This gives inflation of 3.2 per cent.
But look what has happened to the average price level. In the first month, it was 80p - the average of 100p and 60p. In the second month, it was the average of 80p and 80p – also 80p. The average price level hasn’t changed. The Dutot formula tells us that inflation is zero.
This example tells us that there is no such thing as a "true" inflation rate. It depends how you measure it.
At the moment, the ONS uses the Carli formula to calculate RPI, but the Jevons to calculate CPI. For this reason (among others), this is causing RPI inflation to exceed CPI inflation. This is especially true for clothing and footwear. In August, the RPI showed annual inflation of 6.1 per cent in this sector whilst the CPI showed deflation of 0.7 per cent. But the same raw price data is used in both cases. The difference is because of the use of different indices.
Across all prices, the ONS estimates that the "formula effect" caused annual RPI inflation to exceed CPI inflation by 0.88 percentage points last month. And the difference is greater now than a few years ago.
The ONS is considering changing this. If it goes the whole hog and removes all of the formula effect, RPI inflation in future could be almost 0.9 percentage points per year lower than it would otherwise be.
If you have an RPI-linked annuity, this could cost you a lot. If you have £10000 of annuity income today, an annual uprating of 0.88 percentage points less than you’d otherwise get would leave you with an income some £1000 lower in ten years’ time that you’d get under current arrangements.
Now, economists don’t think the ONS will make such a big move. If it were to do so, index-linked gilts, which are linked to the RPI, would become much less attractive. But whilst their prices have fallen in recent weeks, they have not done so by so much as to discount a full move to Jevons indices. It could be that it’s just the clothing component – where the effect is largest – that gets changed.
Do holders of RPI-linked assets have reason to complain about such a change? In one sense no. One could argue that the Carli index has given them too high an increase in incomes in recent years. What the ONS is considering is the removal of an excessive benefit, rather than the imposition of a cost.
But on the other hand, one could argue that an implicit contract is being broken; people bought index-linked gilts and annuities on the assumption that RPI would be calculated as it was. And pensioners could claim that the RPI as it is presently calculated given them a form of rough justice. Because they spend more on things that rise in price (such as fuel) and less on things that fall (such as electronic goods), they face higher inflation than official figures claim. In overstating inflation, the Carli index gives them increases in income to compensate for this.
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Chris blogs at http://stumblingandmumbling.typepad.com