Paasche Index

Abstract

The Paasche index is a composite index number of price arrived at by the weighted sum method. This index number corresponds to the ratio of the sum of the prices of the actual period n and the sum of prices of the reference period 0, these sums being weighted by the respective quantities of the actual period. The Paasche index differs from the Laspeyres index only by the choice of weights method. Indeed, in the Laspeyres index, the weights are given using quantities of the reference period Q 0 rather than those of the current period Q n. HISTORY In the mid-19th century German statistician Paasche, Hermann developed a formula for the index number that carries his name. Paasche, H. (1874) worked on prices recorded in Hamburg. MATHEMATICAL ASPECTS The Paasche index is calculated as follows: I n/0 = P n · Q n P 0 · Q n , where P n and Q n are, respectively, the prices and sold quantities in the current period and P 0 and Q 0 are the prices and sold quantities in the reference period. The sums relate to the considered goods and are expressed in base 100. I n/0 = P n · Q n P 0 · Q n · 100. The Paasche model can also be applied to calculate a quantity index (also called volume index). In this case, it is the prices that are constant and the quantities that are variable: I n/0 = Q n · P n Q 0 · P n · 100. EXAMPLES Consider the following table indicating the respective prices of three food items in reference year 0 and in the current year n, as well as the quantities sold in the current year: Product Price (euros) 1970 1988 Quantity sold in 1988 (Q n) (thousands) (P 0) (P n) Milk 85.5 0.20 1.20 Bread 50.5 0.15 1.10 Butter 40.5 0.50 2.00 From the following table we have: P n Q n = 239.15 and P 0 Q n = 44.925 .