Weighted Aggregate Methods

The simple aggregate index treats every commodity alike. In reality a household spends far more on rice than on, say, matchboxes, so price changes should be weighted by the quantities consumed. In the weighted aggregate methods we multiply each price by an appropriate quantity (weight) before totalling. The methods differ only in which year's quantities they use as weights.

1. Laspeyre's Price Index — base-year quantities as weights ($q_0$):

It answers: 'what would the base-year basket cost now, compared with then?' It tends to overstate the rise in the price level, because it ignores that consumers switch away from goods that have become dearer.

2. Paasche's Price Index — current-year quantities as weights ($q_1$):

It uses the current basket and tends to understate the rise in the price level.

3. Dorbish–Bowley Price Index — the arithmetic mean of Laspeyre's and Paasche's:

By averaging the two it removes some of the upward bias of Laspeyre's and the downward bias of Paasche's.

4. Fisher's Ideal Price Index — the geometric mean of Laspeyre's and Paasche's:

It is called 'ideal' because it uses both base- and current-year quantities and satisfies the time reversal test ($P_{01} \times P_{10} = 1$) and the factor reversal test ($P_{01} \times Q_{01} = V_{01}$) — the only common formula that satisfies both.

5. Marshall–Edgeworth Price Index — the sum of both years' quantities as weights ($q_0 + q_1$): …