# Retail Price Index v Consumer Price Index – or Why Your Pension can Suddenly Shrink.

Author: Andrew McCulloch

The income thresholds for different rates of taxation and the levels of many state benefits usually increase from one year to the next. The main reason given for this is to maintain the real value of taxes and benefits at an approximately constant level. The real value of taxes paid and benefits received reflects the goods and services that can be bought with a given nominal amount of money. Because prices tend to rise from one year to the next, an increase in the nominal value of both taxes and benefits is necessary in order to keep the real value unchanged.

The price level in the economy is usually measured using a price index. Index numbers are values expressed as a percentage of a base figure. So if we use 2010 as a base and prices are 5% higher in 2011, then the price index for 2010 and 2011 is 100 and 105, respectively. The index has no units and this makes it easier to compare different time periods. Price indices are constructed for a group (or basket) of goods and services. The price of each item contributes to the overall index but because some items take up a larger proportion of expenditure than others it is necessary to weight the items. The weights used are commonly either the quantities purchased in a base period or in the current period . For example, the following is an example of a current weighted price index for consumption of champagne and cigars each week where the quantities are in litres/boxes and prices in £ per litre/box:

Prices                        Quantities
2000          2010          2000       2010
Champagne    3              4.5               5            6
Cigars             4              7                  6            9

Expenditure in 2000 based on 2010 quantities
= (price of champagne in 2000 x quantity of champagne in 2010)
+ (price of cigars in 2000 x quantity of cigars in 2010)
= (3 x 6) + (4 x 9)
= 54

Expenditure in 2010
= (price of champagne in 2010 x quantity of champagne in 2010)
+ (price of cigars in 2010 x quantity of cigars in 2010)
= (4.5 x 6) + (7 x 9)
= 90

Index number for 2000 = 54/54 = 100.
Index number for 2010 = 90/54 = 1.66.

There is, however, more than one price index in common use in the UK to measure changes in the price level, or the inflation rate. (The cigar-and-champagne price index, for example, would be a singularly inappropriate index to base the old age pension on.) Since April 2011, the price index used to index most items of government expenditure (tax credits, benefits, public service pensions) has been the consumer prices index (or CPI). Prior to this it was the retail prices index (RPI), and the 2011 budget announced the government's intention to index all direct taxes and contributions using the CPI. Both the CPI and the RPI combine around 180000 prices for 650 representative items [1,2]. Both of them first combine together individual prices to give an average price and then weight these sub-indices together to give an overall index. The main differences between the CPI and RPI are firstly, that the RPI includes some housing costs (house prices and mortgage and council tax payments) that are excluded from the CPI, and secondly the RPI uses the arithmetic mean while the CPI uses the geometric mean to form the price indexes for elementary aggregates.

The Figure shows that, although not always the case, the CPI inflation rate tends to be lower than the corresponding RPI inflation rate. This reflects the tendency for housing costs to increase more rapidly in comparison to the costs of other goods and services and the fact that the geometric mean has to be less than or equal to the arithmetic mean for a given set of prices. The result of using the lower CPI measure of inflation to increase the money value of benefits and pensions is therefore to erode the value of benefits and pensions in real terms. The result of increasing tax thresholds using the CPI is to slowly push more and more people into higher tax brackets - what economists term fiscal drag. The differences between the CPI and RPI might not seem significant but small differences accumulated over time can amount to significant amounts of money. For example, assuming an RPI of 3% and a CPI of 2.33% per annum and a retirement duration of 25 years, the change from RPI to CPI has reduced the value of a public service pension by approximately £30000 [3]. The RPI remains in use, however, to index many items that raise government revenue such as fuel duty and alcohol and tobacco taxes and it is also used to index student loan repayments. This adds around £5000 to the total repayments on a £25000 student loan compared to the repayments that would be made if the loan was indexed using the CPI [4]. The impression is of attempts by the government to raise income and minimise spending in a covert manner. Whether or not that is the case there is a need for greater clarity and public awareness on these issues.

2. Focus on Consumer Price Indices Data for March 2011.
3. Independent Public Service Pensions Commission http://www.hm-treasury.gov.uk/indreview_johnhutton_pensions.htm
4. Using RPI to set student loans will cost graduates up to £5,000 more, says TUC http://www.tuc.org.uk/economy/tuc-19467-f0.cfm

### Optymystic

The result of using the lower CPI measure of inflation to increase the money value of benefits and pensions is therefore to erode the value of benefits and pensions in real terms.

Stats is stats and philosophy is philosophy. while I don't disagree with the sentiment, I strongly suspect that proponents of the CPI model would defend it on the grounds that it is more real than the available alternative. Personally I find this stance highly questionable, but we are not getting sufficient clarity on the case for CPI v RPI other than it suits the government agenda.

### James Wells

I think the RPI and CPI are labelled incorrectly in the graph as currently, the RPI is a higher rate of inflation compared the CPI, and not the other way around as in the chart.

### Rod

So unfortunate you seem to have got the graph wrong. economics again?

### Tony Landau

A very concise and in depth analysis ruined by a suspicious looking graph - why not simply put two tables alongside each other with a third showing the difference over the last 5 years or even the last 10 years. Then what we all know would be very clear - the CPI when used for 'payout' measurement is usually below the RPI.

If there was a choice would any pensioner choose CPI? No!

### James Douglass

What a shame that those who would seek to offer informed advice get the graph on which their data is based so wrong! Why hasn't it been corrected?

2009 is the only year where the RPI was below CPI, so the graph key is wrong. With the exception of 2009, CPI has historically been lower the RPI.

http://www3.hants.gov.uk/finance/retailpricesindexandconsumerpriceindex.htm
http://www.moneyextra.com/dictionary/consumer-price-index-003666.html

### Joe

The black line should definitely be RPI, except for that good article.

### sc

on graph, are the colour labels reversed?

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