AS Macroeconomics / International Economy

Using Index Numbers

Index numbers are a useful way of expressing pieces of information and collections of data. This brief chapter shows you how to express data in index number format and some examples of data which is commonly presented as an index number

Converting data in index number format: Measuring the level of real national output

When we are measuring the level of national income we often make use of index numbers to track what is happening to real GDP. In the table below we see the value of consumer spending and also real GDP expressed in £ billion. I have chosen 1995 as the base year for our index of spending and output. So the data for consumer spending and real GDP has an index value of 100.0 in 1995.

To calculate the index number for consumer spending in 1996 we use the following formula

Index (1996) = (consumer spending (1996) / base year consumer spending) x 100

	Consumer spending	Index of consumer spending	Real GDP	Index of real GDP
	£ billion	1995 = 100	£ billion	1995 = 100
1995 (Base)	512.6	100.0	857.5	100.0
1996	531.9	103.8	880.9	102.7
1997	551.1	107.5	908.7	106.0
1998	572.3	111.6	938.1	109.4
1999	598.8	116.8	966.6	112.7
2000	625.1	121.9	1005.5	117.3
2001	644.9	125.8	1027.9	119.9
2002	667.4	130.2	1048.5	122.3
2003	684.8	133.6	1074.9	125.3
2004	710.2	138.5	1108.9	129.3

One of the advantages of index numbers is that it allows us to compare and contrast more easily different sets of economic data. Consider the information in the table above. Using 1995 as our base year for the index, we can see that consumer spending has grown more quickly than real national income over the period 1995-2003.

Of course the two sets of data are closely linked because consumption accounts for more than 60% of GDP. But the data indicates that consumer demand has been a key factor behind the continuing growth of the economy, indeed consumption as a share of GDP has grown from 60% in 1995 to nearly 65% in 2003 – a record level. Can this consumer boom continue? Much of it has been financed by high rates of borrowing linked to low interest rates and the recent UK housing boom.

Calculating a price index

We will now see how information on prices can be used to create a weighted price index for the economy – this is the sort of data which is then used to calculate the rate of inflation

Category	Price Index	Weighting	Price x Weight
Food	106	18	1908
Alcohol & Tobacco	110	6	660
Clothing	97	12	1164
Transport	103	15	1545
Housing	106	22	2332
Leisure Services	112	9	1008
Household Goods	95	7	665
Other Items	105	11	1155
		100	10437

A weighted price index calculates changes in the average level of prices in the economy. In the hypothetical data shown in the table above we have split consumer spending into eight categories and given each a “weighting” based on the share of total consumer spending given over to each category. So for example, housing and food costs are assumed in our example to take up 40% of total consumer spending. These two items will have a heavy influence on the overall price index.

The price index for each category shows what has happened to the price level since a base year value. To generate a weighted price index we multiply the price index for each category by its weight and then sum these. We then divide by the sum of the weights (100) to find an overall price index (104.37) or 104.4 rounded to one decimal place.

Here is some real world data on a selected of price indices for goods and services in the UK.

	All items	Health	Transport	Communication	Tobacco	Clothing	New Cars	Second Hand Cars
1996	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
2000	105.6	111.6	112.7	89.3	141.2	82.2	99.8	91.2
2003	109.8	124.2	116.9	84.5	158.8	66.8	95.7	85.1

Over the period 1996-2003 there has been a 10% rise in the general price level. But this hides major changes in average prices for different products. The average cost of purchasing tobacco products has jumped by nearly sixty per cent whereas the prices of clothing, second hand cars and communication have been falling.

Author: Geoff Riley, Eton College, September 2006

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AS Macroeconomics / International Economy

Using Index Numbers

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