Walsch’s Weighted Aggregative Method

This method propounded for Index number by Truman L. Kelley is popularly known as Kelley’s method of index number. Mr. Kelley, in his method, takes the quantity of any year, or average of quantities of any number of years as the weights of the items. For this, the method is also otherwise known as the method of fixed weight aggregative index. As such, the formula introduced by Kelley is as under:

 P₀₁(k) = ∑P1q /P0q × 100

Here, q = quantity of any year, or average of quantities of any number of years. Further, such average may be either an arithmetic, or a geometric one.

Thus q may be (q₀+ q1)/ 2

Or √(q₀q1, Or, q₀ Or, q1 etc

Merits

• The chief merits of this method are as follows:
• The weights remain fixed for every time an index is constructed.
• The base period may be changed without changing the weights of the items.
• It is very easy to calculate for which it is the most popular index number.
• It satisfies the time reversal test as the weights remain constant.
• It also satisfies the circular test, and unit test of consistency as the weights are fixed.
• It makes use of all the available data like p₁,p₀,q₁ and q₀.
• It can make use of both arithmetic and geometric means in its calculations.

Demerits

• The chief demerits that go against this method are as follows:
• It may ignore the quantities of both the base year and the current year while taking the weights.
• In comparison to the general weighted index number model i.e. ( ∑P1w / ∑P0w ) x100, this index number model is little more difficult to work out as it may involve all the types of data and two types of average i.e. arithmetic mean, and geometric mean.