Paasche’s Aggregative Method

Passche, a German Mathematician, has introduced this method in 1874 as an improvement over the Laspeyre’s method analysed above. In this method, Mr. Paasche has taken the quantities of the current year as the respective weights of the items in a fixed manner. As such, the formula given by Paasche is as follows:

P₀₁(p) = (∑P1q1 x ∑P0q1) x 100

Where, P01(p) = Paasche’s price index for the current year w.r.t the base year.

∑P1q1 = Total of the products of the price of the current year, and the quantity of the current Year i.e. the aggregate expenditure in the current year on the basis of the quantities in the current year.

∑P0q1 = Total of the products of the price of the base year, and the quantity of the current year i.e. the aggregate expenditure in the base year on the basis of the quantities consumed in the current year.

Merits

The chief merits for which this method is popularly known as the ideal method are as follows:

• It is constructed through geometric mean which is considered most suitable average for an index number.
• It makes use of all possible data relating to an index number viz : P₁, P₀ , q₁ and q₀.
• It counter-balances the effects of upward and downward bias experienced with the method of Laspeyre and Paasche by taking into account both the current year’s and base year’s quantities as the weights.
• It satisfies the unit test, time reversal test and factor reversal test which are analysed little later in detail.
• It reflects the influence of both the current as well as the base year.

Demerits

Despite the above merits, this method also suffers from the following demerits:

• It is very difficult to calculate as it makes use of geometric mean and the logarithms.
• It is not simple to understand by a common man.
• It needs current data relating to prices and quantities every time an index is constructed and hence, it is very expensive and tedious.
• It is difficult to say what exactly it is supposed to measure as it is a hybrid of the two index numbers of Laspeyre and Paasche.