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# The Retail Price Index (RPI)

The Retail Price Index (RPI) was introduced in the UK in 1947, replacing the earlier Cost of Living Index.

Until 2003 – when it was replaced by the internationally recognised Consumer Price Index (CPI) – the RPI was the official index for the measurement of inflation in the UK.

As well as official measure, the RPI also formed the basis for the indexation of many contracts, including pensions, wages, and student grants. It is because of this that the UK still records and publishes the RPI. [1]

## Weaknesses of the RPI

### The formula effect

Fundamentally the RPI suffers because of ‘flawed mathematics’ which means that, as a price index, it has an error built into to its methodology. The relevant element of the methodology is the choice of which formula to use. The RPI uses the Carli formula, which was developed in 1764 by Italian economist, Gian Rinaldo Carli. This formula uses an arithmetic mean to average out price changes in a group or category of good. This, evidently, results in a key statistical bias. With inflation targeting, even a small error translates into a fundamental weakness.

#### Example

If we take the simple example of two shirts, A and B, shirt A increases in price by £10, then falls back by £10 a year later.

Shirt A Shirt B Average % change
2018 £50 £50  -
2019 £60 £50 +20% + 0%/2 = 10%
2020 £50 £50 -16.67% + 0%/2 = -8.33%

The 'flaw' relates to how the averages are calculated. A rise from £50 to £60 is a 20% rise, but a reduction from £60 to £50 is a 16.67% reduction. When averaged between the two goods, the rise is 10%, and the fall is 8.33%. When the two years are averaged out, the result is that prices rise on average - clearly an absurd result. The average percentage change using the RPI formula is (+10 - 8.33/2) is 0.835%. While the price of shirts is identical in 2018 and 2020, using an arithmetic mean clearly produces an inbuilt 'upwards' bias - the so-called 'formula effect' problem. The problem becomes more acute when prices are volatile.

This problem has been written about for over 150 years, including English economist, William Stanley Jevons who, in 1863, criticised the use of an arithmetic mean to develop a price index as they often produced logically inconsistent results. Jevons argued that this problem would be solved by using a geometric mean. [2]

However, in its written submission to the UK Parliament's Economic Affairs Committee - Measuring Inflation, published in 2019, the Royal Statistical Society said:

it was a “fundamental misjudgment” to blame the Carli formula solely for the widening of the formula effect. While the RPI had “clearly over-estimated” the rise in clothing prices in 2010, the Jevons index, (had) probably under-estimates it.” They said none of the index formulas could cope properly with an immense variation in prices (at the time). [3]

Indeed, numerous formulae have been developed to improve the accuracy of price indices. The UK RPI does not rely exclusively on the Carli formula, but also makes use of another arithmetic approach, the Dutot formula, which considers the ratio of average prices in the base year and the current year. The CPI moves away from this approach making use of the geometric Jevons formula.

### Other criticisms of the RPI

1. The original RPI index also produces another problem - that of including housing costs and interest rates. Changes in interest rates will directly impact on housing costs, which create the phenomenon that an increase in interest rates (to reduce inflationary pressure) would increase housing costs (and increase inflationary pressure) - stripping out the policy effect would resolve this issue.

2. The exclusion of the richest and poorest households has led to questions regarding how representative the sample is.

3. Problems with weighting the goods in the basket based on the limited Living Costs and Food Survey rather than a more comprehensive and accurate data source - the national accounts estimates derived from the Household Final Consumption Expenditure data.

In trying to eliminate some of its weakness two versions were introduced – RPIx, which excludes the impact of mortgage interest payments on the inflation rate, and RPIy which excludes mortgage interest and the impact of indirect tax changes.

However, although it is still reported, since 2013 it is not regarded as an official statistic, and from 2030, some RPI reporting will end. Despite its weaknesses, the RPI will survive until 2030 because this is the year the final set of index-linked gilts with an RPI ‘promise’ will mature.

##### Measuring inflation

How do we measure inflation?

##### Demand-pull inflation

What is demand-pull inflation?

##### Supply-side policy

Can supply-side policy reduce inflationary pressure?

[1] More reading on the RPI from the Which Magazine, viewed June 5th 2021

[3] Reported in: https://publications.parliament.uk/pa/ld201719/.html