Chain Index Numbers
In the fixed base technique the base remains same throughout the series of the index. This technique though has certain limitations. As time elapses, the conditions which were once important become less significant and it becomes more difficult to compare accurately the current conditions with those of a remote period. New items may have to be involved and old ones may have to be removed in order to make the index more representatives, in such situations it may be desirable to use the chain base technique. When this technique is used the comparison are not made with a fixed base rather than the changes from year to years. For e.g. For 2009, 2008 will be the base; & for 2008, 2007 will be the base and so on. If however it is desired to associate these relations to a common base the results may be chained to obtain the chain indices. Thus in its uncomplicated form the chain index is one in which the figures for every year (or sub-period thereof) are first expressed as the percentages of the preceding year. These percentages are then chained together by the successive multiplication to form a chain index.
Following are the Steps in constructing a chain index are:
(i) At first express the figures for each year as percentages of the preceding year. The results so obtained are known as link relatives.
(ii) The next step is to chain together these percentages by successive multiplication to form a chain index. The Chain index of any year is the average link relative of that year multiplied by the chain index of previous year divided by 100, in the form of a formula:
Chain index for current year
= average link relative of current year x chain index of previous year / 100
Illustration:
From the following data of the wholesale prices of wheat for ten years construct index numbers taking (a) 2000 as bee and (d) by chain base method.
|
Year
|
Price of wheat ($ per 40 kg.)
|
Year
|
Price of wheat ($ per 40 kg.)
|
|
2000
|
50
|
2005
|
78
|
|
2001
|
60
|
2006
|
82
|
|
2002
|
62
|
2007
|
84
|
|
2003
|
65
|
2008
|
88
|
|
2004
|
70
|
2009
|
90
|
Solution:
Construction of index number taking 2000 as base
|
Year
|
Price of wheat
|
Index number (2000=100)
|
Year
|
Price of wheat
|
Index number (2000=100)
|
|
2000
|
50
|
100
|
2005
|
78
|
78/50x100=156
|
|
2001
|
60
|
60/50x100= 120
|
2006
|
82
|
82/50x100=164
|
|
2002
|
62
|
62/50 x100=124
|
2007
|
84
|
84/40x100=168
|
|
2003
|
65
|
65/50x100=130
|
2008
|
88
|
88/50x100=176
|
|
2004
|
70
|
70/50x100=140
|
2009
|
90
|
90/50x100=180
|
This means that from 2000 to 2001 there is a 20 percent increase and from 2001 to 2002 there is a 24 percent increase and from 2002 to 2003 there is a 30 percent increase. If we are interested in finding out the increase from 2000 to 2001 and from 2001 to 2002 and from 2002 to 2003 we shall have to compute the chain indices.