Measuring the rate: the CPI and the RPI

Overview

Main steps by which the UK inflation rate is measured, base effect in inflation measurement and CPI basket kept representative of what people actually buy.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What are the main steps by which the UK inflation rate is measured?

   Model answer

   A large survey of household spending establishes what a typical household buys, which defines a representative basket of goods and services. Each category in the basket is given a weight in proportion to the share of household spending it accounts for. Price collectors then record thousands of prices for the items in the basket each month, from shops and online. The prices are converted into index numbers and combined using the weights to produce an overall index, and the annual inflation rate is the percentage change in that index compared with the same month a year earlier.

2. 2

   Why is the inflation rate normally compared with the same month a year earlier rather than with the previous month?

   Model answer

   Comparing with the same month a year earlier removes seasonal effects, since prices for items such as clothing, fuel and holidays follow a predictable annual pattern that would otherwise dominate a month-to-month figure. It also smooths short-term noise. The cost is that the figure responds slowly to a change in conditions, and it can be pushed around by what happened twelve months ago rather than by anything happening now, which is known as a base effect.

3. 3

   What is a base effect in inflation measurement?

   Model answer

   A base effect occurs when the annual inflation rate changes because of an unusual movement in the price level a year ago rather than because of anything happening in the current month. If energy prices jumped sharply last year, then once that month drops out of the twelve-month comparison the annual rate falls automatically, even if prices are currently flat. Recognising base effects prevents a fall in the rate being read as evidence that current policy is working.

4. 4

   What are the principal differences between the Consumer Prices Index and the Retail Prices Index?

   Model answer

   The RPI includes several housing costs that the CPI omits, most importantly mortgage interest payments and council tax. The two use different mathematical formulas to combine prices at the most detailed level, with the RPI using an arithmetic mean and the CPI a geometric mean. Their population coverage also differs: the RPI excludes the highest-income households and pensioner households that depend mainly on state pensions and benefits, while the CPI covers all private households and also includes spending by foreign visitors. The CPI is the measure used for the official inflation target.

5. 5

   One item in a basket doubles in price, so its price relative is 200, while another halves, so its price relative is 50. Calculate the arithmetic mean and the geometric mean of the two, and explain what the comparison shows.

   Model answer

   The arithmetic mean is (200 + 50) divided by 2, which equals 125. The geometric mean is the square root of (200 multiplied by 50), which is the square root of 10,000, which equals 100. The arithmetic mean records a 25 per cent rise even though one price doubled and the other exactly halved, while the geometric mean records no change. This gap is the formula effect, and it is the main technical reason the RPI systematically reports a higher rate than the CPI even when both are measuring the same prices.

6. 6

   Why does the geometric mean allow for consumers switching between goods while the arithmetic mean does not?

   Model answer

   When one good becomes relatively dearer, consumers buy less of it and more of a substitute, so the increase in their actual cost of living is smaller than the price rise of the dearer good suggests. The geometric mean has the property of giving less weight to large upward price movements, which approximates that substitution behaviour. The arithmetic mean assumes quantities purchased are unchanged whatever happens to relative prices, so it overstates the rise in the cost of maintaining a given standard of living.

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