Q: I am struggling with index numbers (Part 2)...

... basically when it comes to inflating, deflating changing the base year and weighted index numbers.

... basically when it comes to inflating, deflating changing the base year and weighted index numbers.

(This is Part 2 of the answer, continued from AT, March 2004, page 29. To see Part 1 click the link at the bottom of this page.)

Changing the base year

It is often necessary to change the base year where this is located too far in the past and so becomes meaningless. For example:

Example

 
1998
1999
2000
2001
2002
2003
Index (1976=100)
400
450
478
499
501
550

To change the base date (to rebase), divide each relative by the relative corresponding to the new base time point and multiply the result by 100. So, to change the base to 2000, the result is as follows:

1998
1999
2000
2001
2002
2003
83.6
94.1
100
104.3
104.8
120.5

Weighted Index

A weighted index takes into account that some items are more important than others.

Example

 
2001
2002
2001 (index)
2002 index*
Wages
100,000
105,000
100
105
Rent rates
60,000
66,000
100
110
Materials
250,000
270,000
100
108
Production
100,000
102,000
100
102
Total costs
510,000
543,000
400/4=100
425/4=106

*Costs in 2001/costs in 2002 x 100

However, the above is limited as it takes no account of the weightings of the different costs. To enable this to be done it is necessary to compute the expenditure on each item as follows:

Total wage cost: 100,000/510,000 = 20%

Rent, rates: 60,000/510,000 = 11%

Materials: 250,000/510,000 = 49%

Production costs: 100,000/510,000 = 20%

The index can then be recomputed to take into account the weighting of the individual items as follows:

 
Weighting
2002 index
Weighting 2002 index*
Total wage costs
20%
105
21%
Rent rates
11%
110
12%
Materials
49%
108
53%
Production costs
20%
102
20%
 
106%

*(weighting x 2002 index)

Answered by James Grierson FCCA, FAIA, ACIS, a self-employed consultant

AT, April 2004, page 29

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