Index Numbers

An index number is a specialised statistical figure that measures the average percentage change in a group of related variables — prices, quantities, or values — over time, relative to a chosen base period (whose index value is fixed, by convention, at 100). Because the prices of thousands of individual goods rise and fall by different amounts, and sometimes in different directions, a single summary figure is needed to describe the overall movement of the group as a whole. Index numbers are often called 'economic barometers', since they are the standard tool used to track and compare price levels, the cost of living, industrial production, and the general state of the economy over time.

Types of index numbers commonly studied at the Intermediate level: price index numbers (changes in the general price level of a group of commodities — e.g., the Wholesale Price Index or Consumer Price Index), quantity index numbers (changes in the physical volume of production, sales, or consumption), and value index numbers (changes in total value, i.e., price × quantity, of a group of commodities).

Simple Aggregate Method. The simplest price index sums the current-year prices of all commodities and expresses this as a percentage of the sum of their base-year prices:

where $p_0$ is the base-year price and $p_1$ the current-year price of each commodity. This method treats every commodity as equally important regardless of how much of it is actually bought or sold — its chief weakness, since a high-priced but rarely-bought commodity can distort the index.

Weighted Aggregate Method. To correct this, quantities are used as weights, so commodities that are bought in larger amounts influence the index more. Laspeyres' Method weights every commodity's price by its base-year quantity ($q_0$):

Paasche's Method instead weights by the current-year quantity ($q_1$):

$P_{01}^{P} = \frac{\Sigma p_1 q_1}{\Sigma p_0 q_1} \times 100$ …