Mathematics and Statistics · Ch 13 — Index Numbers
Simple (Unweighted) Aggregate Method
Simple (Unweighted) Aggregate Method
The most direct way to build a price index for a group of commodities is the simple aggregate method. We total the current-year prices of all commodities, total their base-year prices, and express the first total as a percentage of the second:
where is the price index of the current year () with respect to the base year (), is the sum of current-year prices and the sum of base-year prices.
Steps: (i) add up all the base-year prices to get ; (ii) add up all the current-year prices to get ; (iii) substitute in the formula.
Two serious limitations
The simple aggregate method is easy but crude, because:
- It is affected by the units in which prices are quoted — a price 'per quintal' swamps a price 'per kg', so a change in the costly-unit item dominates the index unfairly.
- It gives equal importance to every commodity, ignoring how much of each is actually bought. A rise in the price of a rarely-used luxury counts as much as the same rise in a daily staple. …
— the total of current prices expressed as a percentage of the total of base-year prices, giving ev …