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
