Methods of Constructing Index Numbers
Simple or Unweighted Index Numbers
In unweighted index numbers, the weights are not assigned to the variables, i.e., consideration is not given to the importance of each variable.
The following are different methods followed to calculate the unweighted index numbers.
- Simple aggregative method
Note: The index for the base year is always taken as 100.
Example
Commodities | 1995 | 1996 | 1997 |
A | 13 | 14 | 15.4 |
B | 2 | 2.9 | 3.2 |
C | 7 | 8 | 6.7 |
Total | 22 | 24.9 | 25.3 |
Solution
Simple aggregative index for 1996 over 1995 is
Simple aggregative index for 1997 over 1995 is
Simple aggregative index for 1997 over 1995 is
- Simple average of relatives method
Example
Use the data given in Example 17.1 and find the simple average of relatives for the year 1997, taking 1995 as the base year.
Solution
Given:
Commodities | p_{0} | p_{1} | |
A | 13 | 15.4 | 1.1846 |
B | 2 | 3.2 | 1.60 |
C | 7 | 6.7 | .957 |
Total | 22 | 25.3 | 3.7416 |
Simple average of relatives,
Weighted Index Numbers
In this method, each variable is assigned a weight depending on its relative importance. Often the quantity or the volume of the commodity sold during the base year or some typical year may also be taken as the weights.- Weighted aggregative index method
Note: Laspeyreâ€™s price index number is same as consumer price index number.
Note: Dorbish-Bowley index number is the A.M. of Laspeyreâ€™s and Paascheâ€™s index number.
Example
Compute the Laspeyreâ€™s, Paascheâ€™s, Marshall-Edgeworth and Fisherâ€™s index number for the following data.
Solution
- Weighted aggregative of relatives method
Example
Calculate the weighted arithmetic mean index number from the following data.
Solution
The weighted arithmetic mean index number is
Quantity Index Number
When we want to measure and compare quantities, we resort to quantity index numbers. Quantity indices are used as indicators of the level of output in economy. These are calculated by adopting price as weights, i.e., by changing â€˜pâ€™ into â€˜qâ€™ and â€˜qâ€™ into â€˜pâ€™ in all the formulae for price index number. The various types of quantity indices are as follows:- Simple aggregate of quantities:
- Simple average of quantity relatives:
- Weighted aggregate quantity indices
- Laspeyreâ€™s quantity index number:
- Paascheâ€™s index number:
- Laspeyreâ€™s quantity index number:
Note: Dorbish-Bowley quantity index number is the A.M. of Laspeyreâ€™s and Paascheâ€™s index.
- Marshallâ€“Edgeworth index number:
- Fisherâ€™s ideal index number:
Note: Base year weighted average of quantity relatives is given by
Example
Calculate
- Laspeyreâ€™s quantity index number
- Paascheâ€™s index number
- Dorbishâ€“Bowley quantity index number
- Marshallâ€“Edgeworth index number
- Fisherâ€™s ideal index number for the given data.
Solution
Value Indices
Value is the product of price and quantity. Thus, a value index equals the total sum of the values of given year divided by the sum of the values of base year.
i.e.,
Example
Calculate the value index number for the given data.
Solution